ABOUT GOD

I. By that which is self—caused, I mean that of which the essence involves existence, or that of which the nature is only conceivable as existent.

I. By self-caused, I mean something whose essence includes existence. In other words, its nature makes it impossible to conceive of it as not existing.

II. A thing is called finite after its kind, when it can be limited by another thing of the same nature; for instance, a body is called finite because we always conceive another greater body. So, also, a thought is limited by another thought, but a body is not limited by thought, nor a thought by body.

II. A thing is called finite in its kind when another thing of the same nature can limit it. For example, a body is called finite because we can always imagine a larger body. Similarly, a thought is limited by another thought. But a body is not limited by thought, nor is a thought limited by a body.

III. By substance, I mean that which is in itself, and is conceived through itself: in other words, that of which a conception can be formed independently of any other conception.

III. By substance, I mean something that exists in itself and can be understood through itself. In other words, the concept of substance can be formed independently of any other concept.

IV. By attribute, I mean that which the intellect perceives as constituting the essence of substance.

IV. By attribute, I mean what the intellect perceives as making up the essence of substance.

V. By mode, I mean the modifications¹ of substance, or that which exists in, and is conceived through, something other than itself.

V. By mode, I mean the modifications¹ of substance. In other words, a mode exists in something other than itself and is understood through that other thing.

VI. By God, I mean a being absolutely infinite—that is, a substance consisting in infinite attributes, of which each expresses eternal and infinite essentiality.

VI. By God, I mean an absolutely infinite being. That is, God is a substance with infinitely many attributes. Each attribute expresses an eternal and infinite essence.

Explanation—I say absolutely infinite, not infinite after its kind: for, of a thing infinite only after its kind, infinite attributes may be denied; but that which is absolutely infinite, contains in its essence whatever expresses reality, and involves no negation.

Explanation: I say absolutely infinite, not infinite only within its own kind. For a thing infinite only within its own kind may lack infinitely many attributes. But an absolutely infinite thing contains in its essence everything that expresses reality and involves no negation.

VII. That thing is called free, which exists solely by the necessity of its own nature, and of which the action is determined by itself alone. On the other hand, that thing is necessary, or rather constrained, which is determined by something external to itself to a fixed and definite method of existence or action.

VII. A thing is called free when it exists solely through the necessity of its own nature. Its actions are determined by itself alone. By contrast, a thing is called necessary, or rather constrained, when something external determines its existence or actions. That external influence fixes a specific way for the thing to exist or act.

VIII. By eternity, I mean existence itself, in so far as it is conceived necessarily to follow solely from the definition of that which is eternal.

VIII. By eternity, I mean existence itself, understood as following necessarily and solely from the definition of what is eternal.

Explanation—Existence of this kind is conceived as an eternal truth, like the essence of a thing, and, therefore, cannot be explained by means of continuance or time, though continuance may be conceived without a beginning or end.

Explanation: Existence of this kind is understood as an eternal truth, like the essence of a thing. Therefore, such existence cannot be explained in terms of duration or time. This holds even though duration may be understood as having no beginning or end.

I. Everything which exists, exists either in itself or in something else.

I. Everything that exists exists either in itself or in something else.

II. That which cannot be conceived through anything else must be conceived through itself.

II. Anything that cannot be understood through anything else must be understood through itself.

III. From a given definite cause an effect necessarily follows; and, on the other hand, if no definite cause be granted, it is impossible that an effect can follow.

III. An effect necessarily follows from a given definite cause. Conversely, if no definite cause is given, no effect can follow.

IV. The knowledge of an effect depends on and involves the knowledge of a cause.

IV. Knowledge of an effect depends on and includes knowledge of a cause.

V. Things which have nothing in common cannot be understood, the one by means of the other; the conception of one does not involve the conception of the other.

V. Things that have nothing in common cannot be understood through one another. The concept of one does not involve the concept of the other.

VI. A true idea must correspond with its ideate or object.

VI. A true idea must match the object it represents.

VII. If a thing can be conceived as non—existing, its essence does not involve existence.

VII. If a thing can be conceived as not existing, its essence does not require it to exist.

PROP. I. Substance is by nature prior to its modifications.

PROPOSITION I. Substance is by nature more fundamental than its modifications.

Proof.—This is clear from Deff. iii. and v.

Proof: This is clear from Definitions 3 and 5.

PROP. II. Two substances, whose attributes are different, have nothing in common.

PROP. II. Two substances with different attributes have nothing in common.

Proof.—Also evident from Def. iii. For each must exist in itself, and be conceived through itself; in other words, the conception of one does not imply the conception of the other.

Proof. This is also clear from Definition iii. For each must exist in itself and be understood through itself. In other words, the concept of one does not imply the concept of the other.

PROP. III. Things which have nothing in common cannot be one the cause of the other.

PROP. III. Things that have nothing in common cannot cause one another.

Proof.—If they have nothing in common, it follows that one cannot be apprehended by means of the other (Ax. v.), and, therefore, one cannot be the cause of the other (Ax. iv.). Q.E.D.

Proof. If they have nothing in common, one cannot be understood through the other (Ax. v.). Therefore, one cannot be the cause of the other (Ax. iv.). Q.E.D.

PROP. IV. Two or more distinct things are distinguished one from the other, either by the difference of the attributes of the substances, or by the difference of their modifications.

PROP. IV. Two or more distinct things differ either in the attributes of their substances or in their modifications.

Proof.—Everything which exists, exists either in itself or in something else (Ax. i.),—that is (by Deff. iii. and v.), nothing is granted in addition to the understanding, except substance and its modifications. Nothing is, therefore, given besides the understanding, by which several things may be distinguished one from the other, except the substances, or, in other words (see Ax. iv.), their attributes and modifications. Q.E.D.

Proof. Everything that exists exists either in itself or in something else (Ax. i.). That is, nothing exists outside the understanding except substance and its modifications (Deff. iii. and v.). Therefore, outside the understanding, only substances can provide a basis for distinguishing several things from one another. In other words, only their attributes and modifications can provide such a basis (see Ax. iv.). Q.E.D.

PROP. V. There cannot exist in the universe two or more substances having the same nature or attribute.

PROP. V. No two or more substances in the universe can have the same nature or attribute.

Proof.—If several distinct substances be granted, they must be distinguished one from the other, either by the difference of their attributes, or by the difference of their modifications (Prop. iv.). If only by the difference of their attributes, it will be granted that there cannot be more than one with an identical attribute. If by the difference of their modifications—as substance is naturally prior to its modifications (Prop. i.),—it follows that setting the modifications aside, and considering substance in itself, that is truly, (Deff. iii. and vi.), there cannot be conceived one substance different from another,—that is (by Prop. iv.), there cannot be granted several substances, but one substance only. Q.E.D.

Proof. Suppose several distinct substances exist. They must differ either in their attributes or in their modifications (Prop. iv.). If they differ only in their attributes, we must grant that no two substances can have the same attribute. Suppose instead that they differ in their modifications. Substance is by nature prior to its modifications (Prop. i.). So we must set the modifications aside and consider substance in itself, that is, as it truly is (Deff. iii. and vi.). Considered in this way, one substance cannot be conceived as different from another. Therefore (by Prop. iv.), we cannot grant that several substances exist, but only one substance. Q.E.D.

PROP. VI. One substance cannot be produced by another substance.

PROPOSITION VI. One substance cannot be produced by another substance.

Proof.—It is impossible that there should be in the universe two substances with an identical attribute, i.e. which have anything common to them both (Prop. ii.), and, therefore (Prop. iii.), one cannot be the cause of the other, neither can one be produced by the other. Q.E.D.

Proof. Two substances in the universe cannot have the same attribute, meaning they cannot have anything in common (Prop. ii.). Therefore, neither substance can cause the other, nor can either be produced by the other (Prop. iii.). Q.E.D.

Corollary.—Hence it follows that a substance cannot be produced by anything external to itself. For in the universe nothing is granted, save substances and their modifications (as appears from Ax. i. and Deff. iii. and v.). Now (by the last Prop.) substance cannot be produced by another substance, therefore it cannot be produced by anything external to itself. Q.E.D. This is shown still more readily by the absurdity of the contradictory. For, if substance be produced by an external cause, the knowledge of it would depend on the knowledge of its cause (Ax. iv.), and (by Def. iii.) it would itself not be substance.

Corollary: It follows that a substance cannot be produced by anything outside itself. For nothing exists in the universe except substances and their modifications (as Axiom i and Definitions iii and v show). Now, by the previous proposition, a substance cannot be produced by another substance. Therefore, a substance cannot be produced by anything outside itself. Q.E.D. The same conclusion follows even more easily from the absurdity of the opposite claim. For if a substance were produced by an external cause, knowledge of that substance would depend on knowledge of its cause (Axiom iv). And by Definition iii, such a substance would not itself be a substance.

PROP. VII. Existence belongs to the nature of substances.

PROPOSITION VII. Existence is part of the nature of substances.

Proof.—Substance cannot be produced by anything external (Corollary, Prop vi.), it must, therefore, be its own cause—that is, its essence necessarily involves existence, or existence belongs to its nature.

Proof: Substance cannot be produced by anything external (Corollary to Proposition 6). Therefore, substance must be its own cause. This means its essence necessarily includes existence, or existence belongs to its nature.

PROP. VIII. Every substance is necessarily infinite.

PROPOSITION VIII. Every substance must be infinite.

Proof.—There can only be one substance with an identical attribute, and existence follows from its nature (Prop. vii.); its nature, therefore, involves existence, either as finite or infinite. It does not exist as finite, for (by Def. ii.) it would then be limited by something else of the same kind, which would also necessarily exist (Prop. vii.); and there would be two substances with an identical attribute, which is absurd (Prop. v.). It therefore exists as infinite. Q.E.D.

Proof. Only one substance can have a given attribute, and existence follows from its nature (Prop. vii.). Therefore, the substance’s nature includes existence, either as finite or infinite. The substance cannot be finite. For if it were finite, something else of the same kind would limit it (Def. ii.). That other substance would also necessarily exist (Prop. vii.). There would then be two substances with the same attribute, which is impossible (Prop. v.). Therefore, the substance exists as infinite. Q.E.D.

Note I.—As finite existence involves a partial negation, and infinite existence is the absolute affirmation of the given nature, it follows (solely from Prop. vii.) that every substance is necessarily infinite.

Note I. Finite existence involves a partial negation, while infinite existence is the complete affirmation of a given nature. Therefore, every substance is necessarily infinite. This conclusion follows solely from Proposition vii.

Note II.—No doubt it will be difficult for those who think about things loosely, and have not been accustomed to know them by their primary causes, to comprehend the demonstration of Prop. vii.: for such persons make no distinction between the modifications of substances and the substances themselves, and are ignorant of the manner in which things are produced; hence they may attribute to substances the beginning which they observe in natural objects. Those who are ignorant of true causes, make complete confusion—think that trees might talk just as well as men—that men might be formed from stones as well as from seed; and imagine that any form might be changed into any other. So, also, those who confuse the two natures, divine and human, readily attribute human passions to the deity, especially so long as they do not know how passions originate in the mind. But, if people would consider the nature of substance, they would have no doubt about the truth of Prop. vii. In fact, this proposition would be a universal axiom, and accounted a truism. For, by substance, would be understood that which is in itself, and is conceived through itself—that is, something of which the conception requires not the conception of anything else; whereas modifications exist in something external to themselves, and a conception of them is formed by means of a conception of the thing in which they exist. Therefore, we may have true ideas of non—existent modifications; for, although they may have no actual existence apart from the conceiving intellect, yet their essence is so involved in something external to themselves that they may through it be conceived. Whereas the only truth substances can have, external to the intellect, must consist in their existence, because they are conceived through themselves. Therefore, for a person to say that he has a clear and distinct—that is, a true—idea of a substance, but that he is not sure whether such substance exists, would be the same as if he said that he had a true idea, but was not sure whether or no it was false (a little consideration will make this plain); or if anyone affirmed that substance is created, it would be the same as saying that a false idea was true—in short, the height of absurdity. It must, then, necessarily be admitted that the existence of substance as its essence is an eternal truth. And we can hence conclude by another process of reasoning—that there is but one such substance. I think that this may profitably be done at once; and, in order to proceed regularly with the demonstration, we must premise:——

Note II. People who think loosely and are unused to understanding things through their primary causes will undoubtedly struggle with the proof of Prop. vii. Such people do not distinguish between substances and their modifications. They also do not understand how things are produced. So they may attribute to substances the beginnings they observe in natural objects. Those who do not know the true causes confuse everything. They think trees might talk just as well as humans. They think humans might be formed from stones as well as from seed. And they imagine that any form might change into any other. Likewise, those who confuse divine and human nature readily attribute human passions to God. This is especially true as long as they do not know how passions arise in the mind. But if people considered the nature of substance, they would have no doubt about the truth of Prop. vii. In fact, everyone would accept this proposition as an axiom and regard it as an obvious truth. For they would understand substance as something that exists in itself and is conceived through itself. In other words, the concept of substance requires no concept of anything else. Modifications, however, exist in something other than themselves. We form a concept of modifications through a concept of the thing in which they exist. Therefore, we may have true ideas of modifications that do not exist. Although these modifications may have no actual existence outside the conceiving mind, their essence is bound up with something beyond themselves. Through that other thing, they can be conceived. By contrast, the only truth substances can have outside the mind must consist in their existence, because substances are conceived through themselves. Suppose someone says they have a clear and distinct idea of a substance, that is, a true idea. But they also say they are unsure whether that substance exists. This would be like saying they have a true idea but are unsure whether the idea is false. A little thought will make this clear. Or suppose someone claims that substance is created. This would be like saying that a false idea is true. In short, it would be utterly absurd. We must therefore accept that the existence of substance, like its essence, is an eternal truth. From this, another line of reasoning lets us conclude that there is only one such substance. I think it would be useful to do this now. To proceed with the proof in an orderly way, we must first establish the following:

1. The true definition of a thing neither involves nor expresses anything beyond the nature of the thing defined. From this it follows that——

1. The true definition of a thing neither implies nor states anything beyond the nature of that thing. From this, it follows that:

2. No definition implies or expresses a certain number of individuals, inasmuch as it expresses nothing beyond the nature of the thing defined. For instance, the definition of a triangle expresses nothing beyond the actual nature of a triangle: it does not imply any fixed number of triangles.

2. No definition implies or expresses a fixed number of individuals, because a definition expresses only the nature of the thing defined. For example, the definition of a triangle expresses only the actual nature of a triangle. The definition does not imply any fixed number of triangles.

3. There is necessarily for each individual existent thing a cause why it should exist.

3. For each individual thing that exists, there must be a cause of its existence.

4. This cause of existence must either be contained in the nature and definition of the thing defined, or must be postulated apart from such definition.

4. This cause of existence must lie within the nature and definition of the thing being defined. Otherwise, the cause must be assumed separately from that definition.

It therefore follows that, if a given number of individual things exist in nature, there must be some cause for the existence of exactly that number, neither more nor less. For example, if twenty men exist in the universe (for simplicity's sake, I will suppose them existing simultaneously, and to have had no predecessors), and we want to account for the existence of these twenty men, it will not be enough to show the cause of human existence in general; we must also show why there are exactly twenty men, neither more nor less: for a cause must be assigned for the existence of each individual. Now this cause cannot be contained in the actual nature of man, for the true definition of man does not involve any consideration of the number twenty. Consequently, the cause for the existence of these twenty men, and, consequently, of each of them, must necessarily be sought externally to each individual. Hence we may lay down the absolute rule, that everything which may consist of several individuals must have an external cause. And, as it has been shown already that existence appertains to the nature of substance, existence must necessarily be included in its definition; and from its definition alone existence must be deducible. But from its definition (as we have shown, notes ii., iii.), we cannot infer the existence of several substances; therefore it follows that there is only one substance of the same nature. Q.E.D.

It therefore follows that, if a certain number of individual things exist in nature, their exact number must have a cause. There must be a reason why there are that many, neither more nor less. For example, suppose twenty men exist in the universe. For simplicity, I will suppose they all exist at the same time and have had no predecessors. To explain why these twenty men exist, we cannot simply explain the cause of human existence in general. We must also explain why there are exactly twenty men, neither more nor less. For we must identify a cause for the existence of each individual. Now, this cause cannot lie in human nature itself. The true definition of man says nothing about the number twenty. Consequently, the cause of these twenty men's existence, and therefore of each man's existence, must lie outside each individual. We can therefore state an absolute rule: anything that can consist of several individuals must have an external cause. And, as already shown, existence belongs to the nature of substance. Existence must therefore be included in the definition of substance and must follow from that definition alone. But, as we have shown in notes ii. and iii., that definition cannot imply the existence of several substances. It therefore follows that there is only one substance of the same nature. Q.E.D.

PROP. IX. The more reality or being a thing has, the greater the number of its attributes (Def. iv.).

PROP. IX. The more reality or being a thing has, the more attributes it has (Def. iv.).

PROP. X. Each particular attribute of the one substance must be conceived through itself.

PROP. X. Each individual attribute of the one substance must be understood through itself.

Proof.—An attribute is that which the intellect perceives of substance, as constituting its essence (Def. iv.), and, therefore, must be conceived through itself (Def. iii.). Q.E.D.

Proof: An attribute is what the intellect perceives as constituting the essence of substance (Def. iv.). Therefore, an attribute must be conceived through itself (Def. iii.). Q.E.D.

Note—It is thus evident that, though two attributes are, in fact, conceived as distinct—that is, one without the help of the other—yet we cannot, therefore, conclude that they constitute two entities, or two different substances. For it is the nature of substance that each of its attributes is conceived through itself, inasmuch as all the attributes it has have always existed simultaneously in it, and none could be produced by any other; but each expresses the reality or being of substance. It is, then, far from an absurdity to ascribe several attributes to one substance: for nothing in nature is more clear than that each and every entity must be conceived under some attribute, and that its reality or being is in proportion to the number of its attributes expressing necessity or eternity and infinity. Consequently it is abundantly clear, that an absolutely infinite being must necessarily be defined as consisting in infinite attributes, each of which expresses a certain eternal and infinite essence.

Note: It is therefore clear that two attributes can be understood as distinct, each without reference to the other. Yet we cannot conclude from this distinction that the attributes constitute two entities or two different substances. For substance is by nature such that each of its attributes is understood through itself. All the attributes of substance have always existed together in that substance, and none could be produced by another. Instead, each attribute expresses the reality or being of substance. So it is far from absurd to attribute several attributes to one substance. For nothing in nature is clearer than that every entity must be understood through some attribute. And an entity’s reality or being is proportional to the number of its attributes expressing necessity or eternity and infinity. Consequently, it is abundantly clear that an absolutely infinite being must necessarily be defined as consisting of infinitely many attributes. Each of these attributes expresses a certain eternal and infinite essence.

If anyone now ask, by what sign shall he be able to distinguish different substances, let him read the following propositions, which show that there is but one substance in the universe, and that it is absolutely infinite, wherefore such a sign would be sought in vain.

If anyone now asks what sign distinguishes different substances, they should read the following propositions. These propositions show that there is only one substance in the universe, and that this substance is absolutely infinite. So any search for such a sign would be in vain.

PROP. XI. God, or substance, consisting of infinite attributes, of which each expresses eternal and infinite essentiality, necessarily exists.

PROP. XI. God, or substance, consists of infinitely many attributes. Each attribute expresses an eternal and infinite essence. God necessarily exists.

Proof.—If this be denied, conceive, if possible, that God does not exist: then his essence does not involve existence. But this (Prop. vii.) is absurd. Therefore God necessarily exists.

Proof: If you deny this, imagine, if possible, that God does not exist. Then his essence does not involve existence. But this conclusion is absurd (Proposition 7). Therefore, God necessarily exists.

Another proof.—Of everything whatsoever a cause or reason must be assigned, either for its existence, or for its non—existence—e.g. if a triangle exist, a reason or cause must be granted for its existence; if, on the contrary, it does not exist, a cause must also be granted, which prevents it from existing, or annuls its existence. This reason or cause must either be contained in the nature of the thing in question, or be external to it. For instance, the reason for the non—existence of a square circle is indicated in its nature, namely, because it would involve a contradiction. On the other hand, the existence of substance follows also solely from its nature, inasmuch as its nature involves existence. (See Prop. vii.)

Another proof. For everything, a cause or reason must be given for either its existence or its nonexistence. For example, if a triangle exists, there must be a reason or cause for its existence. If, on the contrary, a triangle does not exist, there must also be a cause preventing or canceling its existence. This reason or cause must lie either within the nature of the thing itself or outside it. For instance, the reason a square circle does not exist lies in its nature, because a square circle involves a contradiction. On the other hand, the existence of substance also follows solely from its nature, because its nature involves existence. (See Prop. vii.)

But the reason for the existence of a triangle or a circle does not follow from the nature of those figures, but from the order of universal nature in extension. From the latter it must follow, either that a triangle necessarily exists, or that it is impossible that it should exist. So much is self—evident. It follows therefrom that a thing necessarily exists, if no cause or reason be granted which prevents its existence.

But the reason a triangle or circle exists does not follow from the nature of those figures. Instead, it follows from the order of universal nature in extension. From that order, either a triangle must necessarily exist, or its existence must be impossible. This much is self-evident. It follows that a thing necessarily exists if there is no cause or reason preventing its existence.

If, then, no cause or reason can be given, which prevents the existence of God, or which destroys his existence, we must certainly conclude that he necessarily does exist. If such a reason or cause should be given, it must either be drawn from the very nature of God, or be external to him—that is, drawn from another substance of another nature. For if it were of the same nature, God, by that very fact, would be admitted to exist. But substance of another nature could have nothing in common with God (by Prop. ii.), and therefore would be unable either to cause or to destroy his existence.

If, then, no cause or reason can prevent God’s existence or destroy it, we must certainly conclude that he necessarily exists. If such a reason or cause could be given, it must come either from God’s own nature or from outside him. An external cause would have to come from another substance with a different nature. For if that substance had the same nature as God, that fact alone would establish that God exists. But a substance with a different nature could have nothing in common with God (by Prop. ii.). Therefore, that substance could neither cause nor destroy his existence.

As, then, a reason or cause which would annul the divine existence cannot be drawn from anything external to the divine nature, such cause must perforce, if God does not exist, be drawn from God's own nature, which would involve a contradiction. To make such an affirmation about a being absolutely infinite and supremely perfect is absurd; therefore, neither in the nature of God, nor externally to his nature, can a cause or reason be assigned which would annul his existence. Therefore, God necessarily exists. Q.E.D.

So no reason or cause preventing God's existence can come from anything outside God's nature. Therefore, if God does not exist, such a cause must come from God's own nature, implying a contradiction. But claiming such a contradiction in an absolutely infinite and supremely perfect being is absurd. Therefore, neither within God's nature nor outside his nature can any cause or reason be given that prevents his existence. Therefore, God necessarily exists. Q.E.D.

Another proof.—The potentiality of non—existence is a negation of power, and contrariwise the potentiality of existence is a power, as is obvious. If, then, that which necessarily exists is nothing but finite beings, such finite beings are more powerful than a being absolutely infinite, which is obviously absurd; therefore, either nothing exists, or else a being absolutely infinite necessarily exists also. Now we exist either in ourselves, or in something else which necessarily exists (see Axiom. i. and Prop. vii.). Therefore a being absolutely infinite—in other words, God (Def. vi.)—necessarily exists. Q.E.D.

Another proof: The ability not to exist is a lack of power. Conversely, the ability to exist is a power, as is obvious. Suppose, then, that only finite beings necessarily exist. Those finite beings would be more powerful than an absolutely infinite being, which is obviously absurd. Therefore, either nothing exists, or an absolutely infinite being also necessarily exists. Now we exist either in ourselves or in something else that necessarily exists (see Axiom i and Proposition vii). Therefore, an absolutely infinite being, in other words, God (Definition vi), necessarily exists. Q.E.D.

Note.—In this last proof, I have purposely shown God's existence à posteriori, so that the proof might be more easily followed, not because, from the same premises, God's existence does not follow à priori. For, as the potentiality of existence is a power, it follows that, in proportion as reality increases in the nature of a thing, so also will it increase its strength for existence. Therefore a being absolutely infinite, such as God, has from himself an absolutely infinite power of existence, and hence he does absolutely exist. Perhaps there will be many who will be unable to see the force of this proof, inasmuch as they are accustomed only to consider those things which flow from external causes. Of such things, they see that those which quickly come to pass—that is, quickly come into existence—quickly also disappear; whereas they regard as more difficult of accomplishment—that is, not so easily brought into existence—those things which they conceive as more complicated.

Note. In the last proof, I deliberately showed God's existence a posteriori, reasoning from effects to causes. I did so to make the proof easier to follow. It was not because God's existence cannot follow a priori, from the same premises. For the capacity to exist is a power. So, the more reality a thing has in its nature, the greater its power to exist. Therefore, an absolutely infinite being, such as God, has in himself an absolutely infinite power to exist. Hence, he does absolutely exist. Perhaps many people will be unable to see the force of this proof. This is because they are accustomed to considering only things that result from external causes. They see that such things quickly disappear when they arise quickly, that is, when they quickly come into existence. By contrast, they regard things they consider more complicated as harder to produce, that is, less easily brought into existence.

However, to do away with this misconception, I need not here show the measure of truth in the proverb, "What comes quickly, goes quickly," nor discuss whether, from the point of view of universal nature, all things are equally easy, or otherwise: I need only remark that I am not here speaking of things, which come to pass through causes external to themselves, but only of substances which (by Prop. vi.) cannot be produced by any external cause. Things which are produced by external causes, whether they consist of many parts or few, owe whatsoever perfection or reality they possess solely to the efficacy of their external cause; and therefore their existence arises solely from the perfection of their external cause, not from their own. Contrariwise, whatsoever perfection is possessed by substance is due to no external cause; wherefore the existence of substance must arise solely from its own nature, which is nothing else but its essence. Thus, the perfection of a thing does not annul its existence, but, on the contrary, asserts it. Imperfection, on the other hand, does annul it; therefore we cannot be more certain of the existence of anything, than of the existence of a being absolutely infinite or perfect—that is, of God. For inasmuch as his essence excludes all imperfection, and involves absolute perfection, all cause for doubt concerning his existence is done away, and the utmost certainty on the question is given. This, I think, will be evident to every moderately attentive reader.

However, to clear up this misconception, I need not examine how true the proverb is: "What comes quickly, goes quickly,". Nor need I discuss whether all things are equally easy from the standpoint of universal nature. I need only point out that I am not discussing things produced by causes outside themselves. I am speaking only of substances, which cannot be produced by any external cause (by Proposition vi.). Things produced by external causes owe all their perfection or reality to the power of their external cause. This holds whether those things have many parts or few. Their existence therefore follows solely from the perfection of their external cause, not from their own perfection. By contrast, whatever perfection substance possesses comes from no external cause. So the existence of substance must follow solely from its own nature, which is simply its essence. Thus, a thing’s perfection does not rule out its existence. On the contrary, perfection affirms existence. Imperfection, on the other hand, rules out existence. Therefore, we cannot be more certain that anything exists than that an absolutely infinite or perfect being exists. That being is God. For his essence excludes all imperfection and includes absolute perfection. This removes every reason to doubt his existence and gives us the greatest possible certainty about it. I think this will be clear to every reader who pays a reasonable amount of attention.

PROP. XII. No attribute of substance can be conceived from which it would follow that substance can be divided.

PROP. XII. No attribute of substance can be understood in a way that implies substance can be divided.

Proof.—The parts into which substance as thus conceived would be divided either will retain the nature of substance, or they will not. If the former, then (by Prop. viii.) each part will necessarily be infinite, and (by Prop. vi.) self—caused, and (by Prop. v.) will perforce consist of a different attribute, so that, in that case, several substances could be formed out of one substance, which (by Prop. vi.) is absurd. Moreover, the parts (by Prop. ii.) would have nothing in common with their whole, and the whole (by Def. iv. and Prop. x.) could both exist and be conceived without its parts, which everyone will admit to be absurd. If we adopt the second alternative—namely, that the parts will not retain the nature of substance—then, if the whole substance were divided into equal parts, it would lose the nature of substance, and would cease to exist, which (by Prop. vii.) is absurd.

Proof. The parts into which substance, understood in this way, would be divided either retain the nature of substance or do not. If the parts retain that nature, each part must be infinite (by Prop. viii.) and self-caused (by Prop. vi.). Each part must also have a different attribute (by Prop. v.). So several substances could be formed from one substance, which is absurd (by Prop. vi.). Moreover, the parts would have nothing in common with the whole (by Prop. ii.). The whole could both exist and be conceived without its parts (by Def. iv. and Prop. x.). Everyone will agree that this is absurd. Now suppose instead that the parts do not retain the nature of substance. Then, if the whole substance were divided into equal parts, it would lose the nature of substance and cease to exist. This is absurd (by Prop. vii.).

PROP. XIII. Substance absolutely infinite is indivisible.

PROP. XIII. Absolutely infinite substance cannot be divided.

Proof.—If it could be divided, the parts into which it was divided would either retain the nature of absolutely infinite substance, or they would not. If the former, we should have several substances of the same nature, which (by Prop. v.) is absurd. If the latter, then (by Prop. vii.) substance absolutely infinite could cease to exist, which (by Prop. xi.) is also absurd.

Proof. If it could be divided, its parts would either retain the nature of absolutely infinite substance or not. If they did, there would be several substances of the same nature. This is absurd (by Prop. v.). If they did not, then absolutely infinite substance could cease to exist (by Prop. vii.). This too is absurd (by Prop. xi.).

Corollary.—It follows, that no substance, and consequently no extended substance, in so far as it is substance, is divisible.

Corollary: It follows that no substance can be divided. Consequently, no extended substance can be divided insofar as it is substance.

Note.—The indivisibility of substance may be more easily understood as follows. The nature of substance can only be conceived as infinite, and by a part of substance, nothing else can be understood than finite substance, which (by Prop. viii) involves a manifest contradiction.

Note: The indivisibility of substance may be easier to understand as follows. Substance can only be conceived as infinite. A part of substance can only mean a finite substance. But finite substance involves an obvious contradiction (by Proposition viii).

PROP. XIV. Besides God no substance can be granted or conceived.

PROP. XIV. No substance other than God can exist or be conceived.

Proof.—As God is a being absolutely infinite, of whom no attribute that expresses the essence of substance can be denied (by Def. vi.), and he necessarily exists (by Prop. xi.); if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by Prop. v.) is absurd; therefore, besides God no substance can be granted, or, consequently, be conceived. If it could be conceived, it would necessarily have to be conceived as existent; but this (by the first part of this proof) is absurd. Therefore, besides God no substance can be granted or conceived. Q.E.D.

Proof. God is an absolutely infinite being. No attribute expressing the essence of substance can be denied of him (by Def. vi.). He also necessarily exists (by Prop. xi.). If any substance besides God existed, it would have to be explained through some attribute of God. There would then be two substances with the same attribute, which is absurd (by Prop. v.). Therefore, no substance besides God can exist or, consequently, be conceived. If such a substance could be conceived, it would necessarily have to be conceived as existing. But the first part of this proof shows that such existence is absurd. Therefore, no substance besides God can exist or be conceived. Q.E.D.

Corollary I.—Clearly, therefore: 1. God is one, that is (by Def. vi.) only one substance can be granted in the universe, and that substance is absolutely infinite, as we have already indicated (in the note to Prop. x.).

Corollary I. Clearly, therefore: 1. God is one. This means (by Definition vi.) that only one substance can exist in the universe, and that substance is absolutely infinite. We have already indicated this in the note to Proposition x.

Corollary II.—It follows: 2. That extension and thought are either attributes of God or (by Ax. i.) accidents (affectiones) of the attributes of God.

Corollary II. 2. Extension and thought are therefore either attributes of God or modifications (affectiones) of God's attributes (by Axiom i.).

PROP. XV. Whatsoever is, is in God, and without God nothing can be, or be conceived.

PROP. XV. Everything that exists is in God. Without God, nothing can exist or be conceived.

Proof.—Besides God, no substance is granted or can be conceived (by Prop. xiv.), that is (by Def. iii.) nothing which is in itself and is conceived through itself. But modes (by Def. v.) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived. But substances and modes form the sum total of existence (by Ax. i.), therefore, without God nothing can be, or be conceived. Q.E.D.

Proof. No substance besides God exists or can be conceived (by Prop. xiv.). That is, nothing besides God exists in itself and is conceived through itself (by Def. iii.). But modes cannot exist or be conceived without substance (by Def. v.). So modes can exist only in the divine nature and can be conceived only through the divine nature. But substances and modes make up everything that exists (by Ax. i.). Therefore, without God nothing can exist or be conceived. Q.E.D.

Note.—Some assert that God, like a man, consists of body and mind, and is susceptible of passions. How far such persons have strayed from the truth is sufficiently evident from what has been said. But these I pass over. For all who have in anywise reflected on the divine nature deny that God has a body. Of this they find excellent proof in the fact that we understand by body a definite quantity, so long, so broad, so deep, bounded by a certain shape, and it is the height of absurdity to predicate such a thing of God, a being absolutely infinite. But meanwhile by other reasons with which they try to prove their point, they show that they think corporeal or extended substance wholly apart from the divine nature, and say it was created by God. Wherefrom the divine nature can have been created, they are wholly ignorant; thus they clearly show, that they do not know the meaning of their own words. I myself have proved sufficiently clearly, at any rate in my own judgment (Coroll. Prop. vi, and note 2, Prop. viii.), that no substance can be produced or created by anything other than itself. Further, I showed (in Prop. xiv.), that besides God no substance can be granted or conceived. Hence we drew the conclusion that extended substance is one of the infinite attributes of God. However, in order to explain more fully, I will refute the arguments of my adversaries, which all start from the following points:——

Note. Some claim that God, like a human being, consists of body and mind and is subject to passions. What has already been said makes it clear how far these people have strayed from the truth. But I will pass over them. For all who have reflected at all on the divine nature deny that God has a body. They find excellent proof in what we mean by a body: a definite quantity with length, breadth, and depth, bounded by a particular shape. It is utterly absurd to attribute such a thing to God, an absolutely infinite being. But the other arguments they use to prove their point reveal something else. They think bodily or extended substance is entirely separate from the divine nature, and say God created it. Yet they have no idea what the divine nature could have been created from. So they clearly show that they do not understand their own words. I have proved that no substance can be produced or created by anything other than itself. At least in my own judgment, I have proved this clearly enough (Coroll. Prop. vi, and note 2, Prop. viii.). Further, I showed (in Prop. xiv.) that no substance besides God can exist or be conceived. From this we concluded that extended substance is one of God's infinite attributes. However, to explain more fully, I will refute my opponents' arguments, all of which begin with the following points:

Extended substance, in so far as it is substance, consists, as they think, in parts, wherefore they deny that it can be infinite, or consequently, that it can appertain to God. This they illustrate with many examples, of which I will take one or two. If extended substance, they say, is infinite, let it be conceived to be divided into two parts; each part will then be either finite or infinite. If the former, then infinite substance is composed of two finite parts, which is absurd. If the latter, then one infinite will be twice as large as another infinite, which is also absurd.

They think that extended substance, insofar as it is substance, consists of parts. So they deny that extended substance can be infinite and, consequently, that it can belong to God. They illustrate this view with many examples, and I will take one or two. If extended substance is infinite, they say, imagine dividing it into two parts. Each part will then be either finite or infinite. If each part is finite, then infinite substance is made up of two finite parts, which is absurd. If each part is infinite, then one infinite will be twice as large as another infinite, which is also absurd.

Further, if an infinite line be measured out in foot lengths, it will consist of an infinite number of such parts; it would equally consist of an infinite number of parts, if each part measured only an inch: therefore, one infinity would be twelve times as great as the other.

Further, if an infinite line is divided into one-foot lengths, the line will contain infinitely many parts. The line would also contain infinitely many parts if each part were only an inch long. Therefore, one infinity would be twelve times as large as the other.

Lastly, if from a single point there be conceived to be drawn two diverging lines which at first are at a definite distance apart, but are produced to infinity, it is certain that the distance between the two lines will be continually increased, until at length it changes from definite to indefinable. As these absurdities follow, it is said, from considering quantity as infinite, the conclusion is drawn, that extended substance must necessarily be finite, and, consequently, cannot appertain to the nature of God.

Lastly, suppose two diverging lines are imagined to extend from a single point. At first, the lines are a definite distance apart, but they extend to infinity. The distance between them will certainly keep increasing until it changes from definite to indefinable. These absurdities are said to follow from treating quantity as infinite. From this, the conclusion is drawn that extended substance must necessarily be finite. Consequently, extended substance cannot belong to the nature of God.

The second argument is also drawn from God's supreme perfection. God, it is said, inasmuch as he is a supremely perfect being, cannot be passive; but extended substance, insofar as it is divisible, is passive. It follows, therefore, that extended substance does not appertain to the essence of God.

The second argument also comes from God's supreme perfection. According to this argument, God cannot be acted upon because he is a supremely perfect being. But extended substance, insofar as it can be divided, can be acted upon. Therefore, extended substance is not part of God's essence.

Such are the arguments I find on the subject in writers, who by them try to prove that extended substance is unworthy of the divine nature, and cannot possibly appertain thereto. However, I think an attentive reader will see that I have already answered their propositions; for all their arguments are founded on the hypothesis that extended substance is composed of parts, and such a hypothesis I have shown (Prop. xii., and Coroll. Prop. xiii.) to be absurd. Moreover, anyone who reflects will see that all these absurdities (if absurdities they be, which I am not now discussing), from which it is sought to extract the conclusion that extended substance is finite, do not at all follow from the notion of an infinite quantity, but merely from the notion that an infinite quantity is measurable, and composed of finite parts therefore, the only fair conclusion to be drawn is that: infinite quantity is not measurable, and cannot be composed of finite parts. This is exactly what we have already proved (in Prop. xii.). Wherefore the weapon which they aimed at us has in reality recoiled upon themselves. If, from this absurdity of theirs, they persist in drawing the conclusion that extended substance must be finite, they will in good sooth be acting like a man who asserts that circles have the properties of squares, and, finding himself thereby landed in absurdities, proceeds to deny that circles have any center, from which all lines drawn to the circumference are equal. For, taking extended substance, which can only be conceived as infinite, one, and indivisible (Props. viii., v., xii.) they assert, in order to prove that it is finite, that it is composed of finite parts, and that it can be multiplied and divided.

These are the arguments I find in writers who claim that extended substance is unworthy of the divine nature. They use these arguments to prove that extended substance cannot possibly belong to that nature. However, I think an attentive reader will see that I have already answered their claims. For all their arguments assume that extended substance is made up of parts. I have shown that assumption to be absurd (Prop. xii., and Coroll. Prop. xiii.). Moreover, anyone who reflects will see that all these supposed absurdities do not follow from the idea of infinite quantity. Whether they really are absurdities is not something I am discussing now. These writers seek to infer from them that extended substance is finite. But the supposed absurdities follow only from assuming that infinite quantity is measurable and made up of finite parts. So the only fair conclusion is this: infinite quantity is not measurable and cannot be made up of finite parts. This is exactly what we have already proved (in Prop. xii.). Thus, the weapon they aimed at us has actually turned against them. Suppose these writers persist in concluding from their own absurd assumption that extended substance must be finite. They would indeed be acting like someone who claims that circles have the properties of squares. On finding that this claim leads to absurdities, he then denies that circles have a center equidistant from every point on the circumference. For extended substance can only be conceived as infinite, one, and indivisible (Props. viii., v., xii.). Yet, to prove that extended substance is finite, they claim it consists of finite parts and can be multiplied and divided.

So, also, others, after asserting that a line is composed of points, can produce many arguments to prove that a line cannot be infinitely divided. Assuredly it is not less absurd to assert that extended substance is made up of bodies or parts, than it would be to assert that a solid is made up of surfaces, a surface of lines, and a line of points. This must be admitted by all who know clear reason to be infallible, and most of all by those who deny the possibility of a vacuum. For if extended substance could be so divided that its parts were really separate, why should not one part admit of being destroyed, the others remaining joined together as before? And why should all be so fitted into one another as to leave no vacuum? Surely in the case of things, which are really distinct one from the other, one can exist without the other, and can remain in its original condition. As, then, there does not exist a vacuum in nature (of which anon), but all parts are bound to come together to prevent it, it follows from this that the parts cannot really be distinguished, and that extended substance in so far as it is substance cannot be divided.

Similarly, others claim that a line consists of points, then offer many arguments proving that a line cannot be infinitely divided. Certainly, claiming that extended substance consists of bodies or parts is no less absurd than making the following claims: a solid consists of surfaces, a surface of lines, and a line of points. Everyone who knows that clear reasoning is infallible must admit this absurdity, especially those who deny that a vacuum is possible. For suppose extended substance could be divided into truly separate parts. Why could one part not be destroyed while the others remained joined together as before? And why should all the parts fit together so perfectly that they leave no vacuum? Surely, when things are truly distinct from one another, one can exist without the other and remain in its original condition. Now, no vacuum exists in nature (more on this later). Instead, all parts must come together to prevent a vacuum. It follows that the parts cannot be truly distinct, and that extended substance, insofar as it is substance, cannot be divided.

If anyone asks me the further question, Why are we naturally so prone to divide quantity? I answer, that quantity is conceived by us in two ways; in the abstract and superficially, as we imagine it; or as substance, as we conceive it solely by the intellect. If, then, we regard quantity as it is represented in our imagination, which we often and more easily do, we shall find that it is finite, divisible, and compounded of parts; but if we regard it as it is represented in our intellect, and conceive it as substance, which it is very difficult to do, we shall then, as I have sufficiently proved, find that it is infinite, one, and indivisible. This will be plain enough to all who make a distinction between the intellect and the imagination, especially if it be remembered, that matter is everywhere the same, that its parts are not distinguishable, except in so far as we conceive matter as diversely modified, whence its parts are distinguished, not really, but modally. For instance, water, in so far as it is water, we conceive to be divided, and its parts to be separated one from the other; but not in so far as it is extended substance; from this point of view it is neither separated nor divisible. Further, water, in so far as it is water, is produced and corrupted; but, in so far as it is substance, it is neither produced nor corrupted.

If anyone asks me further why we are naturally so inclined to divide quantity, my answer is this. We conceive of quantity in two ways. We can view it abstractly and superficially through the imagination, or as substance through the intellect alone. If we view quantity as our imagination presents it, we find it finite, divisible, and made up of parts. We often take this view, and it comes more easily to us. But if we view quantity through the intellect and conceive of it as substance, we find it infinite, one, and indivisible. Conceiving of quantity this way is very difficult, but I have already sufficiently proved this conclusion. This distinction will be clear enough to everyone who distinguishes between the intellect and the imagination. It will be especially clear if we remember that matter is everywhere the same. We can distinguish its parts only insofar as we conceive of matter as modified in different ways. So its parts differ not as separate things, but only in their modes. For example, insofar as water is water, we conceive of it as divided, with its parts separated from one another. But we do not conceive of water this way insofar as it is extended substance. From this perspective, water is neither separated nor divisible. Further, insofar as water is water, it comes into being and passes away. But insofar as water is substance, it neither comes into being nor passes away.

I think I have now answered the second argument; it is, in fact, founded on the same assumption as the first—namely, that matter, in so far as it is substance, is divisible, and composed of parts. Even if it were so, I do not know why it should be considered unworthy of the divine nature, inasmuch as besides God (by Prop. xiv.) no substance can be granted, wherefrom it could receive its modifications. All things, I repeat, are in God, and all things which come to pass, come to pass solely through the laws of the infinite nature of God, and follow (as I will shortly show) from the necessity of his essence. Wherefore it can in nowise be said, that God is passive in respect to anything other than himself, or that extended substance is unworthy of the Divine nature, even if it be supposed divisible, so long as it is granted to be infinite and eternal. But enough of this for the present.

I think I have now answered the second argument. In fact, it rests on the same assumption as the first: matter, as substance, is divisible and made of parts. Even if matter were divisible, I do not know why that would make it unworthy of the divine nature. For, by Proposition xiv, no substance besides God can exist from which matter could receive its modifications. All things, I repeat, are in God. Everything that happens happens solely through the laws of God’s infinite nature. And everything follows necessarily from his essence, as I will show shortly. So God cannot in any way be said to be acted on by anything other than himself. Nor can extended substance be called unworthy of the divine nature, even if we suppose it to be divisible. This holds as long as we acknowledge extended substance to be infinite and eternal. But enough of this for now.

PROP. XVI. From the necessity of the divine nature must follow an infinite number of things in infinite ways—that is, all things which can fall within the sphere of infinite intellect.

PROP. XVI. Infinitely many things must follow in infinitely many ways from the necessity of the divine nature. These are all the things an infinite intellect can grasp.

Proof.—This proposition will be clear to everyone, who remembers that from the given definition of any thing the intellect infers several properties, which really necessarily follow therefrom (that is, from the actual essence of the thing defined); and it infers more properties in proportion as the definition of the thing expresses more reality, that is, in proportion as the essence of the thing defined involves more reality. Now, as the divine nature has absolutely infinite attributes (by Def. vi.), of which each expresses infinite essence after its kind, it follows that from the necessity of its nature an infinite number of things (that is, everything which can fall within the sphere of an infinite intellect) must necessarily follow. Q.E.D.

Proof. This proposition will be clear to anyone who remembers how the intellect draws properties from a thing’s definition. These properties necessarily follow from the actual essence of the thing defined. The more reality the definition expresses, the more properties the intellect draws from it. In other words, the more reality the thing’s essence involves, the more properties follow. Now, the divine nature has absolutely infinite attributes (by Def. vi.). Each attribute expresses an infinite essence of its own kind. Therefore, an infinite number of things must necessarily follow from the necessity of the divine nature. These include everything that can fall within the scope of an infinite intellect. Q.E.D.

Corollary I.—Hence it follows, that God is the efficient cause of all that can fall within the sphere of an infinite intellect.

Corollary I. Therefore, God is the efficient cause of everything an infinite intellect can comprehend.

Corollary II.—It also follows that God is a cause in himself, and not through an accident of his nature.

Corollary II. It also follows that God is inherently a cause, not because of an incidental feature of his nature.

Corollary III.—It follows, thirdly, that God is the absolutely first cause.

Corollary III. Third, it follows that God is the absolutely first cause.

PROP. XVII. God acts solely by the laws of his own nature, and is not constrained by anyone.

PROP. XVII. God acts only according to the laws of his own nature. No one constrains him.

Proof.—We have just shown (in Prop. xvi.), that solely from the necessity of the divine nature, or, what is the same thing, solely from the laws of his nature, an infinite number of things absolutely follow in an infinite number of ways; and we proved (in Prop. xv.), that without God nothing can be nor be conceived but that all things are in God. Wherefore nothing can exist; outside himself, whereby he can be conditioned or constrained to act. Wherefore God acts solely by the laws of his own nature, and is not constrained by anyone. Q.E.D.

Proof. We have just shown (in Prop. xvi.) that infinitely many things necessarily follow from the divine nature in infinitely many ways. They follow solely from the necessity of his nature, or, equivalently, solely from the laws of his nature. We also proved (in Prop. xv.) that nothing can exist or be conceived without God, but all things are in God. So nothing can exist outside God that could determine or compel him to act. Therefore, God acts solely according to the laws of his own nature and is not compelled by anyone. Q.E.D.

Corollary I.—It follows: 1. That there can be no cause which, either extrinsically or intrinsically, besides the perfection of his own nature, moves God to act.

Corollary I. It follows: 1. No cause within or outside God can move him to act except the perfection of his own nature.

Corollary II.—It follows: 2. That God is the sole free cause. For God alone exists by the sole necessity of his nature (by Prop. xi. and Prop. xiv., Coroll. i.), and acts by the sole necessity of his own nature, wherefore God is (by Def. vii.) the sole free cause. Q.E.D.

Corollary II. It follows: 2. God is the only free cause. For God alone exists solely from the necessity of his nature (Proposition XI and Proposition XIV, Corollary I). God also acts solely from the necessity of his own nature. Therefore, by Definition VII, God is the only free cause. Q.E.D.

Note.—Others think that God is a free cause, because he can, as they think, bring it about, that those things which we have said follow from his nature—that is, which are in his power, should not come to pass, or should not be produced by him. But this is the same as if they said, that God could bring it about, that it should follow from the nature of a triangle that its three interior angles should not be equal to two right angles; or that from a given cause no effect should follow, which is absurd.

Note. Others think God is a free cause because they believe he can prevent certain things from happening. These are the things we have said follow from his nature, that is, things within his power. They believe these things could fail to happen or not be produced by him. But this is like saying God could make a triangle’s nature require its three interior angles not to equal two right angles. Or it is like saying God could make a given cause produce no effect. Both claims are absurd.

Moreover, I will show below, without the aid of this proposition, that neither intellect nor will appertain to God's nature. I know that there are many who think that they can show, that supreme intellect and free will do appertain to God's nature; for they say they know of nothing more perfect, which they can attribute to God, than that which is the highest perfection in ourselves. Further, although they conceive God as actually supremely intelligent, they yet do not believe that he can bring into existence everything which he actually understands, for they think that they would thus destroy God's power. If, they contend, God had created everything which is in his intellect, he would not be able to create anything more, and this, they think, would clash with God's omnipotence; therefore, they prefer to asset that God is indifferent to all things, and that he creates nothing except that which he has decided, by some absolute exercise of will, to create. However, I think I have shown sufficiently clearly (by Prop. xvi.), that from God's supreme power, or infinite nature, an infinite number of things—that is, all things have necessarily flowed forth in an infinite number of ways, or always flow from the same necessity; in the same way as from the nature of a triangle it follows from eternity and for eternity, that its three interior angles are equal to two right angles. Wherefore the omnipotence of God has been displayed from all eternity, and will for all eternity remain in the same state of activity. This manner of treating the question attributes to God an omnipotence, in my opinion, far more perfect. For, otherwise, we are compelled to confess that God understands an infinite number of creatable things, which he will never be able to create, for, if he created all that he understands, he would, according to this showing, exhaust his omnipotence, and render himself imperfect. Wherefore, in order to establish that God is perfect, we should be reduced to establishing at the same time, that he cannot bring to pass everything over which his power extends; this seems to be a hypothesis most absurd, and most repugnant to God's omnipotence.

Moreover, I will show below that neither intellect nor will belongs to God's nature, without relying on this proposition. I know many people think they can show that supreme intellect and free will belong to God's nature. They say they know nothing more perfect to attribute to God than the highest perfection in ourselves. Yet although they regard God as supremely intelligent, they do not believe he can create everything he actually understands. They think that allowing him to create everything he understands would destroy his power. They argue that if God had created everything in his intellect, he could create nothing more. They think this limit would conflict with God's omnipotence. So they prefer to say that God is indifferent to all things. They say he creates only what he has decided to create through an absolute act of will. However, I think I have shown clearly enough (in Proposition XVI) that infinitely many things necessarily follow from God's supreme power, or infinite nature. That is, all things have necessarily flowed from God's nature in infinitely many ways, or always flow with that same necessity. In just the same way, a triangle's three interior angles equal two right angles. This follows from the triangle's nature, from eternity and for eternity. So God's omnipotence has been active from all eternity and will remain equally active for all eternity. In my opinion, this way of approaching the question attributes a far more perfect omnipotence to God. Otherwise, we must admit that God understands infinitely many things he could create but will never be able to create. For according to this argument, if he created everything he understands, he would exhaust his omnipotence and make himself imperfect. So, to establish God's perfection, we would also have to establish that he cannot do everything within his power. This seems to be a most absurd assumption, utterly at odds with God's omnipotence.

Further (to say a word here concerning the intellect and the will which we attribute to God), if intellect and will appertain to the eternal essence of God, we must take these words in some significance quite different from those they usually bear. For intellect and will, which should constitute the essence of God, would perforce be as far apart as the poles from the human intellect and will, in fact, would have nothing in common with them but the name; there would be about as much correspondence between the two as there is between the Dog, the heavenly constellation, and a dog, an animal that barks. This I will prove as follows. If intellect belongs to the divine nature, it cannot be in nature, as ours is generally thought to be, posterior to, or simultaneous with the things understood, inasmuch as God is prior to all things by reason of his causality (Prop. xvi., Coroll. i.). On the contrary, the truth and formal essence of things is as it is, because it exists by representation as such in the intellect of God. Wherefore the intellect of God, in so far as it is conceived to constitute God's essence, is, in reality, the cause of things, both of their essence and of their existence. This seems to have been recognized by those who have asserted, that God's intellect, God's will, and God's power, are one and the same. As, therefore, God's intellect is the sole cause of things, namely, both of their essence and existence, it must necessarily differ from them in respect to its essence, and in respect to its existence. For a cause differs from a thing it causes, precisely in the quality which the latter gains from the former.

Further, let me say a word here about the intellect and will we attribute to God. If intellect and will belong to God's eternal essence, these words must mean something quite different from their usual meanings. For an intellect and will constituting God's essence would necessarily be worlds apart from human intellect and will. They would, in fact, have nothing in common but their names. The resemblance would be like that between the Dog, the heavenly constellation, and a dog, an animal that barks. I will prove this as follows. Suppose intellect belongs to the divine nature. Then God's intellect cannot, by nature, come after or exist alongside the things understood, as ours is generally thought to do. For God comes before all things because he causes them (Prop. xvi., Coroll. i.). On the contrary, the truth and formal essence of things are what they are because God's intellect represents them as such. Therefore, God's intellect, understood as constituting God's essence, is actually the cause of both the essence and existence of things. Those who say that God's intellect, will, and power are one and the same seem to have recognized this. God's intellect is therefore the sole cause of things, causing both their essence and their existence. So God's intellect must necessarily differ from those things in both essence and existence. For a cause differs from what it causes in precisely the quality that the effect receives from the cause.

For example, a man is the cause of another man's existence, but not of his essence (for the latter is an eternal truth), and, therefore, the two men may be entirely similar in essence, but must be different in existence; and hence if the existence of one of them cease, the existence of the other will not necessarily cease also; but if the essence of one could be destroyed, and be made false, the essence of the other would be destroyed also. Wherefore, a thing which is the cause both of the essence and of the existence of a given effect, must differ from such effect both in respect to its essence, and also in respect to its existence. Now the intellect of God is the cause both of the essence and the existence of our intellect; therefore, the intellect of God in so far as it is conceived to constitute the divine essence, differs from our intellect both in respect to essence and in respect to existence, nor can it in anywise agree therewith save in name, as we said before. The reasoning would be identical in the case of the will, as anyone can easily see.

For example, one man causes another man to exist, but does not cause the other man’s essence. That essence is an eternal truth. So the two men may be entirely alike in essence, but must be distinct in existence. Thus, if one man ceases to exist, the other will not necessarily cease to exist. But if one man’s essence could be destroyed and made false, the other man’s essence would also be destroyed. Therefore, anything that causes both the essence and the existence of an effect must differ from that effect in both respects. Now God’s intellect causes both the essence and the existence of our intellect. So God’s intellect, understood as constituting the divine essence, differs from our intellect in both essence and existence. As we said before, God’s intellect can have nothing in common with ours except the name. The same reasoning would apply to the will, as anyone can easily see.

PROP. XVIII. God is the indwelling and not the transient cause of all things.

PROP. XVIII. God is the cause of all things from within, not from outside them.

Proof.—All things which are, are in God, and must be conceived through God (by Prop. xv.), therefore (by Prop. xvi., Coroll. i.) God is the cause of those things which are in him. This is our first point. Further, besides God there can be no substance (by Prop. xiv.), that is nothing in itself external to God. This is our second point. God, therefore, is the indwelling and not the transient cause of all things. Q.E.D.

Proof. All things that exist are in God and must be understood through God (by Proposition xv.). Therefore, God is the cause of all things that are in him (by Proposition xvi., Corollary i.). This establishes our first point. Further, no substance can exist besides God (by Proposition xiv.). That is, nothing that exists in itself is external to God. This establishes our second point. God, therefore, is the indwelling cause of all things, not a cause that acts from outside them. Q.E.D.

PROP. XIX. God, and all the attributes of God, are eternal.

PROPOSITION XIX. God and all of God's attributes are eternal.

Proof.—God (by Def. vi.) is substance, which (by Prop. xi.) necessarily exists, that is (by Prop. vii.) existence appertains to its nature, or (what is the same thing) follows from its definition; therefore, God is eternal (by Def. viii.). Further, by the attributes of God we must understand that which (by Def. iv.) expresses the essence of the divine substance—in other words, that which appertains to substance: that, I say, should be involved in the attributes of substance. Now eternity appertains to the nature of substance (as I have already shown in Prop. vii.); therefore, eternity must appertain to each of the attributes, and thus all are eternal. Q.E.D.

Proof. God is substance (by Def. vi.), and substance necessarily exists (by Prop. xi.). This means existence belongs to the nature of substance (by Prop. vii.). In other words, existence follows from the definition of substance. Therefore, God is eternal (by Def. viii.). Further, God's attributes must be understood as expressing the essence of divine substance (by Def. iv.). In other words, whatever belongs to substance must be included in its attributes. Now eternity belongs to the nature of substance, as I have already shown in Prop. vii. Therefore, eternity must belong to each attribute, and so all the attributes are eternal. Q.E.D.

Note.—This proposition is also evident from the manner in which (in Prop. xi.) I demonstrated the existence of God; it is evident, I repeat, from that proof, that the existence of God, like his essence, is an eternal truth. Further (in Prop. xix. of my "Principles of the Cartesian Philosophy"), I have proved the eternity of God, in another manner, which I need not here repeat.

Note. This proposition is also clear from the way I proved God's existence in Proposition xi. That proof shows, I repeat, that God's existence, like his essence, is an eternal truth. Further, I proved God's eternity another way in Proposition xix. of my "Principles of the Cartesian Philosophy". I do not need to repeat that proof here.

PROP. XX. The existence of God and his essence are one and the same.

PROP. XX. God’s existence and his essence are one and the same.

Proof.—God (by the last Prop.) and all his attributes are eternal, that is (by Def. viii.) each of his attributes expresses existence. Therefore the same attributes of God which explain his eternal essence, explain at the same time his eternal existence—in other words, that which constitutes God's essence constitutes at the same time his existence. Wherefore God's existence and God's essence are one and the same. Q.E.D.

Proof. God and all his attributes are eternal (by the previous proposition). This means that each of his attributes expresses existence (by Definition viii). Therefore, the same attributes of God explain both his eternal essence and his eternal existence. In other words, what makes up God's essence also makes up his existence. Therefore, God's existence and God's essence are one and the same. Q.E.D.

Coroll. I.—Hence it follows that God's existence, like his essence, is an eternal truth.

Corollary I: It follows that God's existence, like his essence, is an eternal truth.

Coroll. II—Secondly, it follows that God, and all the attributes of God, are unchangeable. For if they could be changed in respect to existence, they must also be able to be changed in respect to essence—that is, obviously, be changed from true to false, which is absurd.

Corollary II. Secondly, it follows that God and all God's attributes are unchangeable. For if God and all God's attributes could change in existence, they must also be able to change in essence. That would obviously mean changing from true to false, which is absurd.

PROP. XXI. All things which follow from the absolute nature of any attribute of God must always exist and be infinite, or, in other words, are eternal and infinite through the said attribute.

PROP. XXI. All things that follow from the absolute nature of any attribute of God must always exist and be infinite. In other words, they are eternal and infinite through that attribute.

Proof.—Conceive, if it be possible (supposing the proposition to be denied), that something in some attribute of God can follow from the absolute nature of the said attribute, and that at the same time it is finite, and has a conditioned existence or duration; for instance, the idea of God expressed in the attribute thought. Now thought, in so far as it is supposed to be an attribute of God, is necessarily (by Prop. xi.) in its nature infinite. But, in so far as it possesses the idea of God, it is supposed finite. It cannot, however, be conceived as finite, unless it be limited by thought (by Def. ii.); but it is not limited by thought itself, in so far as it has constituted the idea of God (for so far it is supposed to be finite); therefore, it is limited by thought, in so far as it has not constituted the idea of God, which nevertheless (by Prop. xi.) must necessarily exist.

Proof. Suppose the proposition is denied. Imagine, if possible, that something in an attribute of God follows from that attribute’s absolute nature. Suppose also that this thing is finite and has a conditioned existence or duration. Take, for example, the idea of God expressed in the attribute of thought. Now thought, considered as an attribute of God, is necessarily infinite in nature (by Prop. xi.). But thought, insofar as it contains the idea of God, is assumed to be finite. Yet thought cannot be conceived as finite unless it is limited by thought (by Def. ii.). But thought is not limited by thought itself insofar as thought has formed the idea of God. For in that respect, thought is assumed to be finite. Therefore, thought is limited by thought insofar as thought has not formed the idea of God. Nevertheless, this latter thought must necessarily exist (by Prop. xi.).

We have now granted, therefore, thought not constituting the idea of God, and, accordingly, the idea of God does not naturally follow from its nature in so far as it is absolute thought (for it is conceived as constituting, and also as not constituting, the idea of God), which is against our hypothesis. Wherefore, if the idea of God expressed in the attribute thought, or, indeed, anything else in any attribute of God (for we may take any example, as the proof is of universal application) follows from the necessity of the absolute nature of the said attribute, the said thing must necessarily be infinite, which was our first point.

We have therefore now allowed that thought does not constitute the idea of God. Accordingly, the idea of God does not follow naturally from thought’s nature insofar as thought is absolute. For thought is conceived both as constituting the idea of God and as not constituting it. But this contradicts our hypothesis. Therefore, suppose the idea of God, expressed in the attribute of thought, follows necessarily from that attribute’s absolute nature. The same argument applies to anything else in any attribute of God. We may take any example, because the proof applies universally. If something follows necessarily from an attribute’s absolute nature, that thing must necessarily be infinite. This was our first point.

Furthermore, a thing which thus follows from the necessity of the nature of any attribute cannot have a limited duration. For if it can, suppose a thing, which follows from the necessity of the nature of some attribute, to exist in some attribute of God, for instance, the idea of God expressed in the attribute thought, and let it be supposed at some time not to have existed, or to be about not to exist.

Furthermore, a thing that follows necessarily from the nature of any attribute cannot exist for only a limited time. For if it can, suppose such a thing exists in some attribute of God. For example, consider the idea of God expressed in the attribute of thought. Suppose also that this idea did not exist at some time, or is about to stop existing.

Now thought being an attribute of God, must necessarily exist unchanged (by Prop. xi., and Prop. xx., Coroll. ii.); and beyond the limits of the duration of the idea of God (supposing the latter at some time not to have existed, or not to be going to exist) thought would perforce have existed without the idea of God, which is contrary to our hypothesis, for we supposed that, thought being given, the idea of God necessarily flowed therefrom. Therefore the idea of God expressed in thought, or anything which necessarily follows from the absolute nature of some attribute of God, cannot have a limited duration, but through the said attribute is eternal, which is our second point. Bear in mind that the same proposition may be affirmed of anything, which in any attribute necessarily follows from God's absolute nature.

Now thought is an attribute of God, so thought must necessarily exist unchanged (by Prop. xi., and Prop. xx., Coroll. ii.). Suppose the idea of God had not existed at some time, or would cease to exist. Then thought would necessarily have existed beyond that idea’s duration, without the idea of God. But this contradicts our hypothesis. For we supposed that, given thought, the idea of God necessarily followed from thought. Therefore, the idea of God expressed in thought cannot have a limited duration. The same holds for anything that necessarily follows from the absolute nature of any attribute of God. Instead, through that attribute, it is eternal. This establishes our second point. Remember that the same proposition applies to anything that, within any attribute, necessarily follows from God’s absolute nature.

PROP. XXII. Whatsoever follows from any attribute of God, in so far as it is modified by a modification, which exists necessarily and as infinite, through the said attribute, must also exist necessarily and as infinite.

PROP. XXII. Suppose something follows from an attribute of God insofar as that attribute is modified by a modification. If that modification exists necessarily and is infinite through that attribute, the result must also exist necessarily and be infinite.

Proof.—The proof of this proposition is similar to that of the preceding one.

Proof: The proof of this proposition is similar to the proof of the previous proposition.

PROP. XXIII. Every mode, which exists both necessarily and as infinite, must necessarily follow either from the absolute nature of some attribute of God, or from an attribute modified by a modification which exists necessarily, and as infinite.

PROP. XXIII. Every mode that exists necessarily and is infinite must necessarily follow from one of two sources. Either it follows from the absolute nature of some attribute of God. Or it follows from an attribute modified by a modification that itself exists necessarily and is infinite.

Proof.—A mode exists in something else, through which it must be conceived (Def. v.), that is (Prop. xv.), it exists solely in God, and solely through God can be conceived. If therefore a mode is conceived as necessarily existing and infinite, it must necessarily be inferred or perceived through some attribute of God, in so far as such attribute is conceived as expressing the infinity and necessity of existence, in other words (Def. viii.) eternity; that is, in so far as it is considered absolutely. A mode, therefore, which necessarily exists as infinite, must follow from the absolute nature of some attribute of God, either immediately (Prop. xxi.) or through the means of some modification, which follows from the absolute nature of the said attribute; that is (by Prop. xxii.), which exists necessarily and as infinite.

Proof. A mode exists in something else and must be understood through that other thing (Def. v.). That is (Prop. xv.), a mode exists only in God and can be understood only through God. Suppose, then, that a mode is understood as necessarily existing and infinite. Such a mode must necessarily be inferred or perceived through some attribute of God. That attribute must be understood as expressing infinity and necessary existence, or, in other words (Def. viii.), eternity. This means considering the attribute absolutely. Therefore, a mode that necessarily exists as infinite must follow from the absolute nature of some attribute of God. The mode must follow either directly (Prop. xxi.) or through some modification that follows from that attribute’s absolute nature. Such a modification, therefore (Prop. xxii.), exists necessarily and as infinite.

PROP. XXIV. The essence of things produced by God does not involve existence.

PROPOSITION XXIV. The essence of things produced by God does not imply that those things exist.

Proof.—This proposition is evident from Def. i. For that of which the nature (considered in itself) involves existence is self—caused, and exists by the sole necessity of its own nature.

Proof. This proposition follows directly from Definition 1. For anything whose nature, considered in itself, entails existence is self-caused. Such a thing exists solely because its own nature makes its existence necessary.

Corollary.—Hence it follows that God is not only the cause of things coming into existence, but also of their continuing in existence, that is, in scholastic phraseology, God is cause of the being of things (essendi rerum). For whether things exist, or do not exist, whenever we contemplate their essence, we see that it involves neither existence nor duration; consequently, it cannot be the cause of either the one or the other. God must be the sole cause, inasmuch as to him alone does existence appertain. (Prop. xiv. Coroll. i.) Q.E.D.

Corollary. It follows that God causes not only things to come into existence, but also their continued existence. In scholastic terms, God is the cause of the being of things (essendi rerum). For whether things exist or not, whenever we consider their essence, we see that their essence involves neither existence nor duration. Consequently, their essence cannot cause either their existence or their duration. God must be the sole cause, since existence belongs to him alone. (Proposition xiv, Corollary i.) Q.E.D.

PROP. XXV. God is the efficient cause not only of the existence of things, but also of their essence.

PROPOSITION XXV. God is the efficient cause of both the existence of things and their essence.

Proof.—If this be denied, then God is not the cause of the essence of things; and therefore the essence of things can (by Ax. iv.) be conceived without God. This (by Prop. xv.) is absurd. Therefore, God is the cause of the essence of things. Q.E.D.

Proof. If this is denied, then God is not the cause of the essence of things. Therefore, by Axiom iv, the essence of things can be understood without God. By Proposition xv, this conclusion is absurd. Therefore, God is the cause of the essence of things. Q.E.D.

Note.—This proposition follows more clearly from Prop. xvi. For it is evident thereby that, given the divine nature, the essence of things must be inferred from it, no less than their existence—in a word, God must be called the cause of all things, in the same sense as he is called the cause of himself. This will be made still clearer by the following corollary.

Note. This proposition follows more clearly from Proposition 16. For Proposition 16 makes it clear that, given the divine nature, we must infer both the essence and existence of things. In short, God must be called the cause of all things just as he is called the cause of himself. The following corollary will make this point still clearer.

Corollary.—Individual things are nothing but modifications of the attributes of God, or modes by which the attributes of God are expressed in a fixed and definite manner. The proof appears from Prop. xv. and Def. v.

Corollary. Individual things are nothing but modifications of God’s attributes. In other words, they are modes that express God’s attributes in a fixed and definite way. The proof follows from Proposition 15 and Definition 5.

PROP. XXVI. A thing which is conditioned to act in a particular manner, has necessarily been thus conditioned by God; and that which has not been conditioned by God cannot condition itself to act.

PROP. XXVI. Anything determined to act in a particular way has necessarily been determined to do so by God. And anything not determined by God cannot determine itself to act.

Proof.—That by which things are said to be conditioned to act in a particular manner is necessarily something positive (this is obvious); therefore both of its essence and of its existence God by the necessity of his nature is the efficient cause (Props. xxv. and xvi.); this is our first point. Our second point is plainly to be inferred therefrom. For if a thing, which has not been conditioned by God, could condition itself, the first part of our proof would be false, and this, as we have shown is absurd.

Proof. Whatever determines things to act in a particular way is necessarily something positive (this is obvious). Therefore, God is the efficient cause of both the essence and the existence of whatever determines things to act. God causes both through the necessity of his nature (Props. xxv. and xvi.). This establishes our first point. Our second point follows clearly from the first. For if something not determined by God could determine itself, the first part of our proof would be false. But, as we have shown, that would be absurd.

PROP. XXVII. A thing, which has been conditioned by God to act in a particular way, cannot render itself unconditioned.

PROP. XXVII. A thing determined by God to act in a particular way cannot free itself from that determination.

Proof.—This proposition is evident from the third axiom.

Proof: This proposition follows clearly from the third axiom.

PROP. XXVIII. Every individual thing, or everything which is finite and has a conditioned existence, cannot exist or be conditioned to act, unless it be conditioned for existence and action by a cause other than itself, which also is finite, and has a conditioned existence; and likewise this cause cannot in its turn exist, or be conditioned to act, unless it be conditioned for existence and action by another cause, which also is finite, and has a conditioned existence, and so on to infinity.

PROP. XXVIII. Every individual thing is finite and has an existence determined by conditions. No such thing can exist or be determined to act unless another cause determines its existence and action. That cause must also be finite and have an existence determined by conditions. Likewise, that cause cannot itself exist or be determined to act unless another cause determines its existence and action. This further cause must also be finite and have an existence determined by conditions. The same continues to infinity.

Proof.—Whatsoever is conditioned to exist and act, has been thus conditioned by God (by Prop. xxvi. and Prop. xxiv., Coroll.).

Proof. Everything determined to exist and act has been determined by God (by Proposition 26 and Proposition 24, Corollary).

But that which is finite, and has a conditioned existence, cannot be produced by the absolute nature of any attribute of God; for whatsoever follows from the absolute nature of any attribute of God is infinite and eternal (by Prop. xxi.). It must, therefore, follow from some attribute of God, in so far as the said attribute is considered as in some way modified; for substance and modes make up the sum total of existence (by Ax. i. and Def. iii., v.), while modes are merely modifications of the attributes of God. But from God, or from any of his attributes, in so far as the latter is modified by a modification infinite and eternal, a conditioned thing cannot follow. Wherefore it must follow from, or be conditioned for, existence and action by God or one of his attributes, in so far as the latter are modified by some modification which is finite, and has a conditioned existence. This is our first point. Again, this cause or this modification (for the reason by which we established the first part of this proof) must in its turn be conditioned by another cause, which also is finite, and has a conditioned existence, and, again, this last by another (for the same reason); and so on (for the same reason) to infinity. Q.E.D.

But a finite thing whose existence is conditioned cannot be produced by the absolute nature of any attribute of God. For whatever follows from the absolute nature of any attribute of God is infinite and eternal (by Prop. xxi.). So a finite thing must follow from some attribute of God considered as modified in some way. For substance and modes make up everything that exists (by Ax. i. and Def. iii., v.). And modes are simply modifications of God's attributes. But a conditioned thing cannot follow from God, or any of his attributes, insofar as they have an infinite and eternal modification. Therefore, a finite thing must follow from God or one of his attributes insofar as they have a finite modification whose existence is conditioned. That finite modification must determine the thing's existence and action. This establishes our first point. Again, this cause or modification must itself be determined by another cause that is also finite and has a conditioned existence. The reason is the same as in the first part of this proof. And this further cause must, for the same reason, be determined by another cause. This continues to infinity, for the same reason. Q.E.D.

Note.—As certain things must be produced immediately by God, namely those things which necessarily follow from his absolute nature, through the means of these primary attributes, which, nevertheless, can neither exist nor be conceived without God, it follows:—1. That God is absolutely the proximate cause of those things immediately produced by him. I say absolutely, not after his kind, as is usually stated. For the effects of God cannot either exist or be conceived without a cause (Prop. xv. and Prop. xxiv. Coroll.). 2. That God cannot properly be styled the remote cause of individual things, except for the sake of distinguishing these from what he immediately produces, or rather from what follows from his absolute nature. For, by a remote cause, we understand a cause which is in no way conjoined to the effect. But all things which are, are in God, and so depend on God, that without him they can neither be nor be conceived.

Note. Certain things must be produced directly by God. These things necessarily follow from his absolute nature through these primary attributes. Yet these attributes can neither exist nor be conceived without God. It follows: 1. God is, in an absolute sense, the immediate cause of the things he produces directly. I say in an absolute sense, not within his own kind, as is usually said. For God's effects can neither exist nor be conceived without a cause (Prop. xv. and Prop. xxiv. Coroll.). 2. God cannot properly be called the remote cause of individual things, except to distinguish them from what he produces directly. Or rather, the distinction is between individual things and what follows from his absolute nature. For by a remote cause, we mean a cause that is in no way connected to its effect. But everything that exists is in God. All things depend on God so completely that without him they can neither exist nor be conceived.

PROP. XXIX. Nothing in the universe is contingent, but all things are conditioned to exist and operate in a particular manner by the necessity of the divine nature.

PROP. XXIX. Nothing in the universe exists or happens by chance. Instead, the necessity of the divine nature determines that all things exist and act in specific ways.

Proof.—Whatsoever is, is in God (Prop. xv.). But God cannot be called a thing contingent. For (by Prop. xi.) he exists necessarily, and not contingently. Further, the modes of the divine nature follow therefrom necessarily, and not contingently (Prop. xvi.); and they thus follow, whether we consider the divine nature absolutely, or whether we consider it as in any way conditioned to act (Prop. xxvii.). Further, God is not only the cause of these modes, in so far as they simply exist (by Prop. xxiv, Coroll.), but also in so far as they are considered as conditioned for operating in a particular manner (Prop. xxvi.). If they be not conditioned by God (Prop. xxvi.), it is impossible, and not contingent, that they should condition themselves; contrariwise, if they be conditioned by God, it is impossible, and not contingent, that they should render themselves unconditioned. Wherefore all things are conditioned by the necessity of the divine nature, not only to exist, but also to exist and operate in a particular manner, and there is nothing that is contingent. Q.E.D.

Proof. Everything that exists is in God (Prop. xv.). But God cannot be called contingent. For he exists necessarily, not contingently (Prop. xi.). Further, the modes of the divine nature follow necessarily from that nature, not contingently (Prop. xvi.). This holds whether we consider the divine nature in itself or as determined to act in any way (Prop. xxvii.). Further, God causes these modes not only to exist (Prop. xxiv, Coroll.). He also determines them to act in a particular way (Prop. xxvi.). If God does not determine them to act, they cannot determine themselves (Prop. xxvi.). Their inability to do so is necessary, not contingent. Conversely, if God determines them to act, they cannot free themselves from that determination. This inability, too, is necessary, not contingent. Therefore, the necessity of the divine nature determines all things not only to exist, but to exist and act in a particular way. Nothing is contingent. Q.E.D.

Note.—Before going any further, I wish here to explain, what we should understand by nature viewed as active (natura naturans), and nature viewed as passive (natura naturata). I say to explain, or rather call attention to it, for I think that, from what has been said, it is sufficiently clear, that by nature viewed as active we should understand that which is in itself, and is conceived through itself, or those attributes of substance, which express eternal and infinite essence, in other words (Prop. xiv., Coroll. i., and Prop. xvii., Coroll. ii) God, in so far as he is considered as a free cause.

Note. Before going further, I want to explain nature viewed as active (natura naturans) and nature viewed as passive (natura naturata). I say explain, but I should rather say draw attention to these meanings. For I think what has already been said makes the meaning of nature viewed as active clear enough. We should understand it as what exists in itself and is understood through itself. Or we should understand it as those attributes of substance that express eternal and infinite essence. In other words, it is God, considered as a free cause (Prop. xiv., Coroll. i., and Prop. xvii., Coroll. ii).

By nature viewed as passive I understand all that which follows from the necessity of the nature of God, or of any of the attributes of God, that is, all the modes of the attributes of God, in so far as they are considered as things which are in God, and which without God cannot exist or be conceived.

By nature viewed as passive, I mean everything that follows necessarily from the nature of God or any of God's attributes. That is, I mean all the modes of God's attributes, considered as things that are in God. Without God, these things cannot exist or be conceived.

PROP. XXX. Intellect, in function (actu) finite, or in function infinite, must comprehend the attributes of God and the modifications of God, and nothing else.

PROP. XXX. The intellect in action (actu), whether finite or infinite, must understand God's attributes and modifications, and nothing else.

Proof.—A true idea must agree with its object (Ax. vi.); in other words (obviously), that which is contained in the intellect in representation must necessarily be granted in nature. But in nature (by Prop. xiv., Coroll. i.) there is no substance save God, nor any modifications save those (Prop. xv.) which are in God, and cannot without God either be or be conceived. Therefore the intellect, in function finite, or in function infinite, must comprehend the attributes of God and the modifications of God, and nothing else. Q.E.D.

Proof. A true idea must agree with its object (Ax. vi.). In other words, obviously, whatever the intellect represents must necessarily exist in nature. But in nature there is no substance except God (Prop. xiv., Coroll. i.). Nor are there any modifications except those in God (Prop. xv.). These modifications cannot exist or be conceived without God. Therefore, whether functioning finitely or infinitely, the intellect must comprehend God's attributes and modifications, and nothing else. Q.E.D.

PROP. XXXI. The intellect in function, whether finite or infinite, as will, desire, love, &c., should be referred to passive nature and not to active nature.

PROP. XXXI. The intellect in operation, whether finite or infinite, should be understood as part of passive nature, not active nature. The same applies to will, desire, love, and so on.

Proof.—By the intellect we do not (obviously) mean absolute thought, but only a certain mode of thinking, differing from other modes, such as love, desire, &c., and therefore (Def. v.) requiring to be conceived through absolute thought. It must (by Prop. xv. and Def. vi.), through some attribute of God which expresses the eternal and infinite essence of thought, be so conceived, that without such attribute it could neither be nor be conceived. It must therefore be referred to nature passive rather than to nature active, as must also the other modes of thinking. Q.E.D.

Proof. By intellect we obviously do not mean absolute thought, but only a particular mode of thinking. This mode differs from other modes, such as love, desire, and so on. Therefore (Def. v.), the intellect must be understood through absolute thought. By Prop. xv. and Def. vi., the intellect must be understood through some attribute of God. This attribute expresses the eternal and infinite essence of thought. Without this attribute, the intellect could neither exist nor be understood. The intellect must therefore belong to nature passive rather than nature active, as must the other modes of thinking. Q.E.D.

Note.—I do not here, by speaking of intellect in function, admit that there is such a thing as intellect in potentiality: but, wishing to avoid all confusion, I desire to speak only of what is most clearly perceived by us, namely, of the very act of understanding, than which nothing is more clearly perceived. For we cannot perceive anything without adding to our knowledge of the act of understanding.

Note. When I speak here of the intellect in action, I do not mean that an intellect exists in potential form. But to avoid all confusion, I want to speak only of what we perceive most clearly: the act of understanding itself. Nothing is perceived more clearly than this act. For we cannot perceive anything without adding to our knowledge of the act of understanding.

PROP. XXXII. Will cannot be called a free cause, but only a necessary cause.

PROPOSITION XXXII. The will cannot be called a free cause, but only a necessary cause.

Proof.—Will is only a particular mode of thinking, like intellect; therefore (by Prop. xxviii.) no volition can exist, nor be conditioned to act, unless it be conditioned by some cause other than itself, which cause is conditioned by a third cause, and so on to infinity. But if will be supposed infinite, it must also be conditioned to exist and act by God, not by virtue of his being substance absolutely infinite, but by virtue of his possessing an attribute which expresses the infinite and eternal essence of thought (by Prop. xxiii.). Thus, however it be conceived, whether as finite or infinite, it requires a cause by which it should be conditioned to exist and act. Thus (Def. vii.) it cannot be called a free cause, but only a necessary or constrained cause. Q.E.D.

Proof. Will, like intellect, is only a particular mode of thinking. Therefore (by Prop. xxviii.), no act of will can exist or be determined to act without a cause beyond itself. That cause must be determined by a third cause, and so on to infinity. But suppose will is infinite. Even then, God must determine will to exist and act. God does so not because he is an absolutely infinite substance. Rather, God does so because he possesses an attribute expressing the infinite and eternal essence of thought (by Prop. xxiii.). Thus, whether will is understood as finite or infinite, will requires a cause determining its existence and action. Thus (Def. vii.), will cannot be called a free cause, but only a necessary or constrained cause. Q.E.D.

Coroll. I.—Hence it follows, first, that God does not act according to freedom of the will.

Corollary I. First, it follows that God does not act out of free will.

Coroll. II.—It follows, secondly, that will and intellect stand in the same relation to the nature of God as do motion, and rest, and absolutely all natural phenomena, which must be conditioned by God (Prop. xxix.) to exist and act in a particular manner. For will, like the rest, stands in need of a cause, by which it is conditioned to exist and act in a particular manner. And although, when will or intellect be granted, an infinite number of results may follow, yet God cannot on that account be said to act from freedom of the will, any more than the infinite number of results from motion and rest would justify us in saying that motion and rest act by free will. Wherefore will no more appertains to God than does anything else in nature, but stands in the same relation to him as motion, rest, and the like, which we have shown to follow from the necessity of the divine nature, and to be conditioned by it to exist and act in a particular manner.

Coroll. II. Secondly, will and intellect relate to God’s nature just as motion, rest, and absolutely all natural phenomena do. All must be determined by God to exist and act in a particular way (Prop. xxix.). For will, like everything else, needs a cause that determines it to exist and act in a particular way. Although infinitely many results may follow if will or intellect is granted, God cannot therefore be said to act by free will. Infinitely many results also follow from motion and rest, but these results do not justify saying motion and rest act by free will. Therefore, will belongs to God no more than anything else in nature does. Instead, will relates to God just as motion, rest, and similar phenomena do. As we have shown, these phenomena follow necessarily from God’s nature. God’s nature determines them to exist and act in a particular way.

PROP. XXXIII. Things could not have been brought into being by God in any manner or in any order different from that which has in fact obtained.

PROP. XXXIII. God could not have brought things into existence in any other way or order than he actually did.

Proof—All things necessarily follow from the nature of God (Prop. xvi.), and by the nature of God are conditioned to exist and act in a particular way (Prop. xxix.). If things, therefore, could have been of a different nature, or have been conditioned to act in a different way, so that the order of nature would have been different, God's nature would also have been able to be different from what it now is; and therefore (by Prop. xi.) that different nature also would have perforce existed, and consequently there would have been able to be two or more Gods. This (by Prop. xiv., Coroll. i.) is absurd. Therefore things could not have been brought into being by God in any other manner, &c. Q.E.D.

Proof: All things necessarily follow from God's nature (Prop. xvi.). God's nature determines that all things exist and act in a particular way (Prop. xxix.). Suppose, then, that things could have had a different nature or been determined to act differently. If so, the order of nature would have been different. God's nature would then also have been able to differ from what it now is. And therefore, by Prop. xi., that different nature would necessarily have existed too. Consequently, there could have been two or more Gods. But the existence of two or more Gods is absurd (Prop. xiv., Coroll. i.). Therefore, God could not have brought things into being in any other way, etc. Q.E.D.

Note I.—As I have thus shown, more clearly than the sun at noonday, that there is nothing to justify us in calling things contingent, I wish to explain briefly what meaning we shall attach to the word contingent; but I will first explain the words necessary and impossible.

Note I. I have shown, more clearly than the midday sun, that we have no reason to call things contingent. I now wish to explain briefly what we will mean by the word contingent. But first I will explain the words necessary and impossible.

A thing is called necessary either in respect to its essence or in respect to its cause; for the existence of a thing necessarily follows, either from its essence and definition, or from a given efficient cause. For similar reasons a thing is said to be impossible; namely, inasmuch as its essence or definition involves a contradiction, or because no external cause is granted, which is conditioned to produce such an effect; but a thing can in no respect be called contingent, save in relation to the imperfection of our knowledge.

A thing is called necessary either because of its essence or because of its cause. For its existence necessarily follows either from its essence and definition or from a given efficient cause. For similar reasons, a thing is called impossible. Either its essence or definition contains a contradiction, or no external cause exists with the conditions needed to produce it. But a thing can be called contingent only because our knowledge is incomplete.

A thing of which we do not know whether the essence does or does not involve a contradiction, or of which, knowing that it does not involve a contradiction, we are still in doubt concerning the existence, because the order of causes escapes us,—such a thing, I say, cannot appear to us either necessary or impossible. Wherefore we call it contingent or possible.

Suppose we do not know whether a thing's essence involves a contradiction. Or suppose we know its essence involves no contradiction, but still doubt whether the thing exists. In the second case, we doubt because we do not understand the order of causes. In either case, such a thing, I say, cannot seem to us either necessary or impossible. So we call it contingent or possible.

Note II.—It clearly follows from what we have said, that things have been brought into being by God in the highest perfection, inasmuch as they have necessarily followed from a most perfect nature. Nor does this prove any imperfection in God, for it has compelled us to affirm his perfection. From its contrary proposition, we should clearly gather (as I have just shown), that God is not supremely perfect, for if things had been brought into being in any other way, we should have to assign to God a nature different from that, which we are bound to attribute to him from the consideration of an absolutely perfect being.

Note II. From what we have said, it clearly follows that God brought things into being with the highest perfection. For things necessarily followed from a supremely perfect nature. This necessity does not show any imperfection in God. On the contrary, it has forced us to affirm his perfection. The opposite claim would clearly imply that God is not supremely perfect, as I have just shown. For if things had come into being in any other way, we would have to give God a different nature. That nature would differ from the one we must attribute to him when considering an absolutely perfect being.

I do not doubt, that many will scout this idea as absurd, and will refuse to give their minds up to contemplating it, simply because they are accustomed to assign to God a freedom very different from that which we (Def. vii.) have deduced. They assign to him, in short, absolute free will. However, I am also convinced that if such persons reflect on the matter, and duly weigh in their minds our series of propositions, they will reject such freedom as they now attribute to God, not only as nugatory, but also as a great impediment to organized knowledge. There is no need for me to repeat what I have said in the note to Prop. xvii. But, for the sake of my opponents, I will show further, that although it be granted that will pertains to the essence of God, it nevertheless follows from his perfection, that things could not have been by him created other than they are, or in a different order; this is easily proved, if we reflect on what our opponents themselves concede, namely, that it depends solely on the decree and will of God, that each thing is what it is. If it were otherwise, God would not be the cause of all things. Further, that all the decrees of God have been ratified from all eternity by God himself. If it were otherwise, God would be convicted of imperfection or change. But in eternity there is no such thing as when, before, or after; hence it follows solely from the perfection of God, that God never can decree, or never could have decreed anything but what is; that God did not exist before his decrees, and would not exist without them. But, it is said, supposing that God had made a different universe, or had ordained other decrees from all eternity concerning nature and her order, we could not therefore conclude any imperfection in God. But persons who say this must admit that God can change his decrees. For if God had ordained any decrees concerning nature and her order, different from those which he has ordained—in other words, if he had willed and conceived something different concerning nature—he would perforce have had a different intellect from that which he has, and also a different will. But if it were allowable to assign to God a different intellect and a different will, without any change in his essence or his perfection, what would there be to prevent him changing the decrees which he has made concerning created things, and nevertheless remaining perfect? For his intellect and will concerning things created and their order are the same, in respect to his essence and perfection, however they be conceived.

I have no doubt that many will dismiss this idea as absurd and refuse to consider it. They will do so simply because they are used to attributing a very different kind of freedom to God. Their view differs from the freedom we have established (Def. vii.). In short, they attribute absolute free will to him. Yet I am also convinced that these people will reject their view if they reflect and carefully weigh our propositions. They will reject the freedom they now attribute to God as not only meaningless but a major obstacle to systematic knowledge. I need not repeat what I said in the note to Prop. xvii. But for my opponents’ sake, I will show something further. Even if we grant that will belongs to God’s essence, his perfection still has a necessary consequence. He could not have created things differently or in a different order. We can easily prove this by considering what our opponents themselves concede. They concede that each thing is what it is solely because of God’s decree and will. Otherwise, God would not be the cause of all things. They also concede that God himself has confirmed all his decrees from all eternity. Otherwise, God would be shown to be imperfect or subject to change. But in eternity there is no when, before, or after. God’s perfection alone therefore means that he can never decree, and could never have decreed, anything other than what exists. God did not exist before his decrees, and he would not exist without them. But some object that God might have made a different universe. Or he might have established different decrees from all eternity concerning nature and its order. They argue that neither possibility would imply any imperfection in God. But those who say this must admit that God can change his decrees. Suppose God had established different decrees concerning nature and its order from those he has established. In other words, suppose he had willed and conceived something different concerning nature. Then he would necessarily have had a different intellect and a different will. But suppose we could attribute a different intellect and will to God without changing his essence or perfection. What, then, would prevent him from changing his decrees concerning created things while remaining perfect? For however we conceive his intellect and will concerning created things and their order, their relation to his essence and perfection remains the same.

Further, all the philosophers whom I have read admit that God's intellect is entirely actual, and not at all potential; as they also admit that God's intellect, and God's will, and God's essence are identical, it follows that, if God had had a different actual intellect and a different will, his essence would also have been different; and thus, as I concluded at first, if things had been brought into being by God in a different way from that which has obtained, God's intellect and will, that is (as is admitted) his essence would perforce have been different, which is absurd.

Further, all the philosophers I have read agree that God's intellect is entirely actual, not potential. They also agree that God's intellect, will, and essence are identical. So, if God had had a different actual intellect and a different will, his essence would also have been different. Thus, as I first concluded, if God had brought things into being differently, his intellect and will would necessarily have been different. His essence would therefore also have been different, since, as these philosophers agree, his intellect, will, and essence are identical. But that conclusion is absurd.

As these things could not have been brought into being by God in any but the actual way and order which has obtained; and as the truth of this proposition follows from the supreme perfection of God; we can have no sound reason for persuading ourselves to believe that God did not wish to create all the things which were in his intellect, and to create them in the same perfection as he had understood them.

God could only have brought these things into existence in the way and order that actually occurred. This truth follows from God's supreme perfection. So we have no sound reason to believe that God did not wish to create all the things in his intellect, with the same perfection with which he understood them.

But, it will be said, there is in things no perfection nor imperfection; that which is in them, and which causes them to be called perfect or imperfect, good or bad, depends solely on the will of God. If God had so willed, he might have brought it about that what is now perfection should be extreme imperfection, and vice versâ. What is such an assertion, but an open declaration that God, who necessarily understands that which he wishes, might bring it about by his will, that he should understand things differently from the way in which he does understand them? This (as we have just shown) is the height of absurdity. Wherefore, I may turn the argument against its employers, as follows:—All things depend on the power of God. In order that things should be different from what they are, God's will would necessarily have to be different. But God's will cannot be different (as we have just most clearly demonstrated) from God's perfection. Therefore neither can things be different. I confess, that the theory which subjects all things to the will of an indifferent deity, and asserts that they are all dependent on his fiat, is less far from the truth than the theory of those, who maintain that God acts in all things with a view of promoting what is good. For these latter persons seem to set up something beyond God, which does not depend on God, but which God in acting looks to as an exemplar, or which he aims at as a definite goal. This is only another name for subjecting God to the dominion of destiny, an utter absurdity in respect to God, whom we have shown to be the first and only free cause of the essence of all things and also of their existence. I need, therefore, spend no time in refuting such wild theories.

But someone will say that things have no perfection or imperfection in themselves. Whatever makes us call them perfect or imperfect, good or bad, depends solely on God's will. If God had willed otherwise, he could have made what is now perfection into extreme imperfection, and vice versa. But what does this claim amount to? God necessarily understands what he wills. Yet this claim openly declares that God could will himself to understand things differently from how he actually understands them. As we have just shown, this is utterly absurd. So I can turn the argument against those who use it: All things depend on God's power. For things to be different from what they are, God's will would necessarily have to be different. But God's will cannot differ from God's perfection, as we have just demonstrated with complete clarity. Therefore, things cannot be different either. I admit that one theory comes closer to the truth than another. The first subjects all things to the will of a God who chooses without preference. It claims that everything depends on his command. The second holds that God acts in everything to promote what is good. Those who hold the second theory seem to place something beyond God that does not depend on him. They make this something a model God follows when acting, or a definite goal he aims to reach. This is just another way of subjecting God to the rule of fate. Such a claim is utterly absurd when applied to God. We have shown that God is the first and only free cause of both the essence and existence of all things. So I need not spend any time refuting such wild theories.

PROP. XXXIV. God's power is identical with his essence.

PROPOSITION XXXIV. God's power is the same as his essence.

Proof.—From the sole necessity of the essence of God it follows that God is the cause of himself (Prop. xi.) and of all things (Prop. xvi. and Coroll.). Wherefore the power of God, by which he and all things are and act, is identical with his essence. Q.E.D.

Proof. God is the cause of himself solely because of the necessity of his essence (Prop. xi.). For the same reason, God is also the cause of all things (Prop. xvi. and Coroll.). Therefore, God's power, through which he and all things exist and act, is identical with his essence. Q.E.D.

PROP. XXXV. Whatsoever we conceive to be in the power of God, necessarily exists.

PROP. XXXV. Whatever we understand to be within God's power necessarily exists.

Proof.—Whatsoever is in God's power, must (by the last Prop.) be comprehended in his essence in such a manner, that it necessarily follows therefrom, and therefore necessarily exists. Q.E.D.

Proof: By the previous proposition, everything in God's power must be contained in his essence and follow necessarily from it. Therefore, everything in God's power necessarily exists. Q.E.D.

PROP. XXXVI. There is no cause from whose nature some effect does not follow.

PROP. XXXVI. Every cause has some effect that follows from its nature.

Proof.—Whatsoever exists expresses God's nature or essence in a given conditioned manner (by Prop. xxv., Coroll.); that is, (by Prop. xxxiv.), whatsoever exists, expresses in a given conditioned manner God's power, which is the cause of all things, therefore an effect must (by Prop. xvi.) necessarily follow. Q.E.D.

Proof. Everything that exists expresses God's nature or essence in a specific, conditioned way (by Prop. xxv., Coroll.). That is, everything that exists expresses God's power in a specific, conditioned way (by Prop. xxxiv.). God's power is the cause of all things, so an effect must necessarily follow (by Prop. xvi.). Q.E.D.

In the foregoing I have explained the nature and properties of God. I have shown that he necessarily exists, that he is one: that he is, and acts solely by the necessity of his own nature; that he is the free cause of all things, and how he is so; that all things are in God, and so depend on him, that without him they could neither exist nor be conceived; lastly, that all things are predetermined by God, not through his free will or absolute fiat, but from the very nature of God or infinite power. I have further, where occasion afforded, taken care to remove the prejudices, which might impede the comprehension of my demonstrations. Yet there still remain misconceptions not a few, which might and may prove very grave hindrances to the understanding of the concatenation of things, as I have explained it above. I have therefore thought it worth while to bring these misconceptions before the bar of reason.

So far, I have explained God’s nature and properties. I have shown that he necessarily exists and that he is one. He exists and acts solely from the necessity of his own nature. I have shown that he is the free cause of all things, and explained how this is so. All things are in God and depend on him. Without him, nothing could exist or be conceived. Finally, I have shown that all things are predetermined by God. This follows not from his free will or absolute command, but from God’s very nature, or infinite power. I have also taken opportunities to clear away prejudices that might prevent readers from understanding my proofs. Yet many misconceptions remain. These misconceptions could, and may still, seriously obstruct an understanding of how things are linked together, as I explained above. I have therefore thought it worthwhile to examine these misconceptions in the light of reason.

All such opinions spring from the notion commonly entertained, that all things in nature act as men themselves act, namely, with an end in view. It is accepted as certain, that God himself directs all things to a definite goal (for it is said that God made all things for man, and man that he might worship him). I will, therefore, consider this opinion, asking first, why it obtains general credence, and why all men are naturally so prone to adopt it? secondly, I will point out its falsity; and, lastly, I will show how it has given rise to prejudices about good and bad, right and wrong, praise and blame, order and confusion, beauty and ugliness, and the like. However, this is not the place to deduce these misconceptions from the nature of the human mind: it will be sufficient here, if I assume as a starting point, what ought to be universally admitted, namely, that all men are born ignorant of the causes of things, that all have the desire to seek for what is useful to them, and that they are conscious of such desire. Herefrom it follows, first, that men think themselves free inasmuch as they are conscious of their volitions and desires, and never even dream, in their ignorance, of the causes which have disposed them so to wish and desire. Secondly, that men do all things for an end, namely, for that which is useful to them, and which they seek. Thus it comes to pass that they only look for a knowledge of the final causes of events, and when these are learned, they are content, as having no cause for further doubt. If they cannot learn such causes from external sources, they are compelled to turn to considering themselves, and reflecting what end would have induced them personally to bring about the given event, and thus they necessarily judge other natures by their own. Further, as they find in themselves and outside themselves many means which assist them not a little in the search for what is useful, for instance, eyes for seeing, teeth for chewing, herbs and animals for yielding food, the sun for giving light, the sea for breeding fish, &c., they come to look on the whole of nature as a means for obtaining such conveniences. Now as they are aware, that they found these conveniences and did not make them, they think they have cause for believing, that some other being has made them for their use. As they look upon things as means, they cannot believe them to be self—created; but, judging from the means which they are accustomed to prepare for themselves, they are bound to believe in some ruler or rulers of the universe endowed with human freedom, who have arranged and adapted everything for human use. They are bound to estimate the nature of such rulers (having no information on the subject) in accordance with their own nature, and therefore they assert that the gods ordained everything for the use of man, in order to bind man to themselves and obtain from him the highest honor. Hence also it follows, that everyone thought out for himself, according to his abilities, a different way of worshipping God, so that God might love him more than his fellows, and direct the whole course of nature for the satisfaction of his blind cupidity and insatiable avarice. Thus the prejudice developed into superstition, and took deep root in the human mind; and for this reason everyone strove most zealously to understand and explain the final causes of things; but in their endeavor to show that nature does nothing in vain, i.e. nothing which is useless to man, they only seem to have demonstrated that nature, the gods, and men are all mad together. Consider, I pray you, the result: among the many helps of nature they were bound to find some hindrances, such as storms, earthquakes, diseases, &c.: so they declared that such things happen, because the gods are angry at some wrong done to them by men, or at some fault committed in their worship. Experience day by day protested and showed by infinite examples, that good and evil fortunes fall to the lot of pious and impious alike; still they would not abandon their inveterate prejudice, for it was more easy for them to class such contradictions among other unknown things of whose use they were ignorant, and thus to retain their actual and innate condition of ignorance, than to destroy the whole fabric of their reasoning and start afresh. They therefore laid down as an axiom, that God's judgments far transcend human understanding. Such a doctrine might well have sufficed to conceal the truth from the human race for all eternity, if mathematics had not furnished another standard of verity in considering solely the essence and properties of figures without regard to their final causes. There are other reasons (which I need not mention here) besides mathematics, which might have caused men's minds to be directed to these general prejudices, and have led them to the knowledge of the truth.

All these opinions come from a common belief: everything in nature acts as humans do, with a goal in mind. People take it as certain that God himself directs everything toward a definite goal. For they say that God made everything for humans, and made humans so that they would worship him. I will therefore examine this opinion. First, I will ask why people generally believe it and why all humans are naturally so inclined to adopt it. Second, I will show that it is false. Finally, I will show how it has produced prejudices about good and bad, right and wrong, praise and blame, order and confusion, beauty and ugliness, and similar things. But this is not the place to trace these misconceptions to the nature of the human mind. Here, it will be enough to begin with something everyone ought to admit. All humans are born ignorant of the causes of things. All desire to seek what is useful to them, and all are conscious of that desire. Two things follow from this. First, people think they are free because they are conscious of their choices and desires. In their ignorance, they never even imagine the causes that have led them to choose and desire as they do. Second, people do everything for a goal, namely, to obtain what is useful to them and what they seek. As a result, they seek only to know the purposes behind events. Once they learn those purposes, they are satisfied and see no reason for further doubt. If they cannot learn these purposes from outside sources, they must turn to themselves. They consider what goal would have led them to bring about the event themselves. In this way, they inevitably judge the nature of other things by their own nature. People also find many things, both within and outside themselves, that greatly help them obtain what is useful. For example, they find eyes for seeing, teeth for chewing, plants and animals for food, and the sun for light. They also find the sea for breeding fish, and so on. So they come to see all of nature as a means of obtaining these benefits. They know that they found these useful things and did not make them. So they think they have reason to believe that some other being made these things for their use. Because they see things as means to an end, they cannot believe that these things created themselves. Instead, they judge them by the means they are accustomed to preparing for themselves. They therefore feel compelled to believe in some ruler or rulers of the universe endowed with human freedom. These rulers, they believe, have arranged and adapted everything for human use. Since people know nothing about these rulers, they must judge the rulers’ nature by their own. They therefore claim that the gods arranged everything for human use to bind humans to them and receive the highest honor. As a result, everyone devised a different way of worshipping God, according to their abilities. Each hoped that God would love them more than others. Each also hoped that God would direct all of nature to satisfy their blind desires and endless greed. In this way, the prejudice grew into superstition and took deep root in the human mind. For this reason, everyone tried with the greatest eagerness to understand and explain the purposes of things. They tried to show that nature does nothing in vain, meaning nothing that is useless to humans. But they seem only to have shown that nature, the gods, and humans are all mad together. Consider, I ask you, the result. Among nature’s many benefits, people were bound to find some obstacles, such as storms, earthquakes, diseases, and so on. So they declared that these things happened because the gods were angry. The gods, they said, were angry at some human wrong against them or some fault in the way people worshipped them. Day after day, experience contradicted this belief. Countless examples showed that good and bad fortune fall on the devout and the irreligious alike. Still, people would not abandon their deeply rooted prejudice. They found it easier to place these contradictions among other unexplained things whose uses they did not know. In this way, they could remain in the ignorance they were born into and still lived in. That was easier than tearing down their entire system of reasoning and starting again. So they declared it a self-evident truth that God’s judgments are far beyond human understanding. Such a doctrine might well have hidden the truth from the human race forever, had mathematics not provided another standard of truth. Mathematics considers only the nature and properties of figures, without regard to their purposes. Besides mathematics, there are other reasons that might have drawn people’s attention to these general prejudices and led them to truth. I need not mention those reasons here.

I have now sufficiently explained my first point. There is no need to show at length, that nature has no particular goal in view, and that final causes are mere human figments. This, I think, is already evident enough, both from the causes and foundations on which I have shown such prejudice to be based, and also from Prop. xvi., and the Corollary of Prop. xxxii., and, in fact, all those propositions in which I have shown, that everything in nature proceeds from a sort of necessity, and with the utmost perfection. However, I will add a few remarks, in order to overthrow this doctrine of a final cause utterly. That which is really a cause it considers as an effect, and vice versâ: it makes that which is by nature first to be last, and that which is highest and most perfect to be most imperfect. Passing over the questions of cause and priority as self—evident, it is plain from Props. xxi., xxii., xxiii. that the effect is most perfect which is produced immediately by God; the effect which requires for its production several intermediate causes is, in that respect, more imperfect. But if those things which were made immediately by God were made to enable him to attain his end, then the things which come after, for the sake of which the first were made, are necessarily the most excellent of all.

I have now explained my first point well enough. There is no need to explain at length that nature has no particular goal in view. Nor need I show that final causes, or purposes, are merely human inventions. I think both points are already clear enough from the causes and foundations of this prejudice, which I have explained. They are also clear from Proposition xvi., the Corollary to Proposition xxxii., and all the other relevant propositions. In those propositions, I have shown that everything in nature follows from a kind of necessity, with the utmost perfection. However, I will add a few remarks to refute the doctrine of final causes completely. This doctrine treats an actual cause as an effect, and an actual effect as a cause. It puts last what is naturally first. It also makes what is highest and most perfect into what is most imperfect. I will leave aside the questions of cause and priority, since the answers are self-evident. Propositions xxi., xxii., and xxiii. clearly show that the most perfect effect is one produced directly by God. An effect requiring several intermediate causes is less perfect in that respect. But suppose God made the things he produced directly in order to achieve his goal. Then the later things, for whose sake the first things were made, must necessarily be the most excellent of all.

Further, this doctrine does away with the perfection of God: for, if God acts for an object, he necessarily desires something which he lacks. Certainly, theologians and metaphysicians draw a distinction between the object of want and the object of assimilation; still they confess that God made all things for the sake of himself, not for the sake of creation. They are unable to point to anything prior to creation, except God himself, as an object for which God should act, and are therefore driven to admit (as they clearly must), that God lacked those things for whose attainment he created means, and further that he desired them.

Further, this doctrine denies God's perfection. For if God acts for a purpose, he must desire something he lacks. Admittedly, theologians and metaphysicians distinguish between a goal of satisfying a need and a goal of assimilation. Still, they acknowledge that God made all things for his own sake, not for the sake of creation. Before creation, they can point to nothing except God himself as a goal for God's actions. So they are forced to admit (as they clearly must) that God lacked the things he created means to obtain. They must also admit that he desired those things.

We must not omit to notice that the followers of this doctrine, anxious to display their talent in assigning final causes, have imported a new method of argument in proof of their theory—namely, a reduction, not to the impossible, but to ignorance; thus showing that they have no other method of exhibiting their doctrine. For example, if a stone falls from a roof on to someone's head, and kills him, they will demonstrate by their new method, that the stone fell in order to kill the man; for, if it had not by God's will fallen with that object, how could so many circumstances (and there are often many concurrent circumstances) have all happened together by chance? Perhaps you will answer that the event is due to the facts that the wind was blowing, and the man was walking that way. "But why," they will insist, "was the wind blowing, and why was the man at that very time walking that way?" If you again answer, that the wind had then sprung up because the sea had begun to be agitated the day before, the weather being previously calm, and that the man had been invited by a friend, they will again insist: "But why was the sea agitated, and why was the man invited at that time?" So they will pursue their questions from cause to cause, till at last you take refuge in the will of God—in other words, the sanctuary of ignorance. So, again, when they survey the frame of the human body, they are amazed; and being ignorant of the causes of so great a work of art, conclude that it has been fashioned, not mechanically, but by divine and supernatural skill, and has been so put together that one part shall not hurt another.

We must also notice how the followers of this doctrine try to prove their theory. Eager to show their talent for explaining things by their purposes, they have introduced a new method of argument. They reduce an argument not to an impossibility, but to ignorance. In doing so, they show that they have no other way to present their doctrine. For example, suppose a stone falls from a roof onto someone's head and kills him. Using their new method, they will prove that the stone fell in order to kill the man. For unless God had willed the stone to fall for that purpose, how could so many circumstances have coincided by chance? There are often many circumstances involved. Perhaps you will answer that the wind was blowing and the man was walking that way. "But why," they will insist, "was the wind blowing, and why was the man walking that way at that very moment?" You might answer that the wind had risen because the sea had become rough the day before, after calm weather. You might also explain that a friend had invited the man. They will insist again: "But why had the sea become rough, and why was the man invited at that time?" So they will keep asking about one cause after another, until you finally take refuge in God's will. In other words, you take refuge in the sanctuary of ignorance. Likewise, when they examine the structure of the human body, they are amazed. Because they do not know the causes of such a great work of art, they draw a conclusion. The body, they conclude, was formed not through mechanical processes, but through divine and supernatural skill. They also conclude that its parts were arranged so that no part would harm another.

Hence anyone who seeks for the true causes of miracles, and strives to understand natural phenomena as an intelligent being, and not to gaze at them like a fool, is set down and denounced as an impious heretic by those, whom the masses adore as the interpreters of nature and the gods. Such persons know that, with the removal of ignorance, the wonder which forms their only available means for proving and preserving their authority would vanish also. But I now quit this subject, and pass on to my third point.

So anyone who seeks the true causes of miracles is branded and denounced as a godless heretic. The same goes for anyone who tries to understand natural phenomena intelligently, rather than stare at them like a fool. The accusers are those whom the masses worship as interpreters of nature and the gods. These interpreters know that once ignorance disappears, so will the wonder that alone lets them establish and maintain their authority. But I now leave this subject and move on to my third point.

After men persuaded themselves, that everything which is created is created for their sake, they were bound to consider as the chief quality in everything that which is most useful to themselves, and to account those things the best of all which have the most beneficial effect on mankind. Further, they were bound to form abstract notions for the explanation of the nature of things, such as goodness, badness, order, confusion, warmth, cold, beauty, deformity, and so on; and from the belief that they are free agents arose the further notions of praise and blame, sin and merit.

Once people convinced themselves that everything was created for their sake, they inevitably judged things by their usefulness to themselves. They saw this usefulness as the most important quality in everything. And they considered the things that benefited humanity most to be the best of all. They also inevitably formed abstract ideas to explain the nature of things. These included goodness, badness, order, confusion, warmth, cold, beauty, deformity, and so on. And their belief that they acted freely gave rise to further ideas of praise and blame, sin and merit.

I will speak of these latter hereafter, when I treat of human nature; the former I will briefly explain here.

I will discuss the latter later, when I discuss human nature. I will briefly explain the former here.

Everything which conduces to health and the worship of God they have called good, everything which hinders these objects they have styled bad; and inasmuch as those who do not understand the nature of things do not verify phenomena in any way, but merely imagine them after a fashion, and mistake their imagination for understanding, such persons firmly believe that there is an order in things, being really ignorant both of things and their own nature. When phenomena are of such a kind, that the impression they make on our senses requires little effort of imagination, and can consequently be easily remembered, we say that they are well—ordered; if the contrary, that they are ill—ordered or confused. Further, as things which are easily imagined are more pleasing to us, men prefer order to confusion—as though there were any order in nature, except in relation to our imagination—and say that God has created all things in order; thus, without knowing it, attributing imagination to God, unless, indeed, they would have it that God foresaw human imagination, and arranged everything, so that it should be most easily imagined. If this be their theory, they would not, perhaps, be daunted by the fact that we find an infinite number of phenomena, far surpassing our imagination, and very many others which confound its weakness. But enough has been said on this subject. The other abstract notions are nothing but modes of imagining, in which the imagination is differently affected: though they are considered by the ignorant as the chief attributes of things, inasmuch as they believe that everything was created for the sake of themselves; and, according as they are affected by it, style it good or bad, healthy or rotten and corrupt. For instance, if the motion which objects we see communicate to our nerves be conducive to health, the objects causing it are styled beautiful; if a contrary motion be excited, they are styled ugly.

They have called everything that promotes health and the worship of God good. They have called everything that hinders these aims bad. People who do not understand the nature of things do not examine phenomena to establish what they are. Instead, they merely imagine phenomena in their own way and mistake their imagination for understanding. Because of this, such people firmly believe that things have an order. In reality, they understand neither things nor their own nature. When sensory impressions require little effort to imagine, and can therefore be easily remembered, we call the phenomena well ordered. When the opposite is true, we call the phenomena badly ordered or confused. Moreover, because things that are easy to imagine please us more, people prefer order to confusion. They act as though nature had any order apart from its relation to our imagination. They say that God created all things in order. In doing so, they unknowingly attribute imagination to God. Unless, indeed, they mean that God foresaw human imagination and arranged everything so we could imagine everything most easily. If this is their theory, perhaps even the following fact would not trouble them. We find infinitely many phenomena that far exceed our imagination, and many others that overwhelm its limited powers. But enough has been said on this subject. The other abstract notions are simply ways of imagining, in which the imagination is affected differently. Yet people who lack understanding consider these notions the chief attributes of things. They do so because they believe everything was created for their sake. Depending on how things affect them, they call those things good or bad, healthy or rotten and corrupt. For example, the objects we see transmit motion to our nerves. If that motion promotes health, we call the objects causing it beautiful. If those objects produce the opposite motion, we call them ugly.

Things which are perceived through our sense of smell are styled fragrant or fetid; if through our taste, sweet or bitter, full—flavored or insipid; if through our touch, hard or soft, rough or smooth, &c.

We call things we perceive through smell fragrant or foul-smelling. If we perceive things through taste, we call them sweet or bitter, full-flavored or bland. If we perceive things through touch, we call them hard or soft, rough or smooth, and so on.

Whatsoever affects our ears is said to give rise to noise, sound, or harmony. In this last case, there are men lunatic enough to believe, that even God himself takes pleasure in harmony; and philosophers are not lacking who have persuaded themselves, that the motion of the heavenly bodies gives rise to harmony—all of which instances sufficiently show that everyone judges of things according to the state of his brain, or rather mistakes for things the forms of his imagination. We need no longer wonder that there have arisen all the controversies we have witnessed, and finally skepticism: for, although human bodies in many respects agree, yet in very many others they differ; so that what seems good to one seems bad to another; what seems well ordered to one seems confused to another; what is pleasing to one displeases another, and so on. I need not further enumerate, because this is not the place to treat the subject at length, and also because the fact is sufficiently well known. It is commonly said: "So many men, so many minds; everyone is wise in his own way; brains differ as completely as palates." All of which proverbs show, that men judge of things according to their mental disposition, and rather imagine than understand: for, if they understood phenomena, they would, as mathematicians attest, be convinced, if not attracted, by what I have urged.

Whatever affects our ears is said to produce noise, sound, or harmony. Some people are mad enough to believe that even God himself takes pleasure in harmony. Nor is there any shortage of philosophers who have convinced themselves that the movements of heavenly bodies produce harmony. All these examples show clearly enough that everyone judges things according to the state of their brain. Or rather, everyone mistakes the products of their imagination for the things themselves. We need no longer wonder at all the disputes we have witnessed, or at the skepticism that eventually followed. For although human bodies are alike in many ways, they differ in very many others. So what seems good to one person seems bad to another. What seems well ordered to one seems confused to another. What pleases one displeases another, and so on. I need not list further examples, because this is not the place to discuss the subject at length. Besides, the fact is well known. People commonly say: "As many people, as many minds. Everyone is wise in their own way. Brains differ just as much as tastes." All these sayings show that people judge things according to their mental disposition, and imagine rather than understand. For if people understood phenomena, my arguments would convince them, even if those arguments did not appeal to them. Mathematicians bear this out.

We have now perceived, that all the explanations commonly given of nature are mere modes of imagining, and do not indicate the true nature of anything, but only the constitution of the imagination; and, although they have names, as though they were entities, existing externally to the imagination, I call them entities imaginary rather than real; and, therefore, all arguments against us drawn from such abstractions are easily rebutted.

We have now seen that all common explanations of nature are merely ways of imagining. These explanations reveal nothing about the true nature of anything, but only how the imagination is formed. Although these imagined things have names as if they existed outside the imagination, I call them imaginary rather than real. Therefore, all arguments against us based on such abstractions are easily refuted.

Many argue in this way. If all things follow from a necessity of the absolutely perfect nature of God, why are there so many imperfections in nature? such, for instance, as things corrupt to the point of putridity, loathsome deformity, confusion, evil, sin, &c. But these reasoners are, as I have said, easily confuted, for the perfection of things is to be reckoned only from their own nature and power; things are not more or less perfect, according as they delight or offend human senses, or according as they are serviceable or repugnant to mankind. To those who ask why God did not so create all men, that they should be governed only by reason, I give no answer but this: because matter was not lacking to him for the creation of every degree of perfection from highest to lowest; or, more strictly, because the laws of his nature are so vast, as to suffice for the production of everything conceivable by an infinite intelligence, as I have shown in Prop. xvi.

Many people argue as follows. If everything follows necessarily from God’s absolutely perfect nature, why are there so many imperfections in nature? Examples include things rotting to the point of putrefaction, disgusting deformities, confusion, evil, sin, and so on. But as I have said, these arguments are easily refuted. For the perfection of things must be judged only by their own nature and power. Things are not more or less perfect because they please or offend human senses, or help or harm humanity. Some ask why God did not create all people so that they would be guided only by reason. I give only this answer: because he had no shortage of material for creating every degree of perfection, from highest to lowest. Or, more precisely, because the laws of his nature are so vast that they can produce everything an infinite intelligence can conceive. I have shown this in Proposition XVI.

Such are the misconceptions I have undertaken to note; if there are any more of the same sort, everyone may easily dissipate them for himself with the aid of a little reflection.

These are the misconceptions I set out to point out. If there are others of the same kind, anyone can easily clear them up with a little reflection.